darmstadt university of technology- 1 - sequential verification by symbolic simulation darmstadt...
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Darmstadt University of Technology - 1 -
Sequential Verification by Symbolic Simulation
Darmstadt University of Technology Dept. of Electrical and Computer Engineering
Germany
Gerd Ritter
Darmstadt University of Technology - 2 -
(if 78rf[adrB] b, x mem[adr2]);twert ( mem[adr2]); (if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe
erweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]); mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2 78 mem[adr1]vawerwesrwaerwearwerwerwerawerawerwarwearl);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778ewrwerawer ewvtroiejwcro[iwehjnr[occwn3r[oweictweticwopjertijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gergeroigtjer[ognifd;lindzgher[tjisereartoearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
tijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gergeroigtjer[ognifd;lindzgher[tjisereartoearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
(if 78r adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 f[adrB] b, x mem[adr2]);twert ( mem[adr2]); (if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe
erweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]); mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if i68i 778 then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);(if adrA adrBertetioerptkerotk8iperot
(if 78rf[adrB] b, x mem[adr2]);twert ( mem[adr2]); (if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2 78 mem[adr1]vawerwesrwaerwearwerwerwerawerawerwarwearl);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778ewrwerawer ewvtroiejwcro[iwehjnr[occwn3r[oweictweticwopjertijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gergeroigtjer[ognifd;lindzgher[tjisereartoearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
(if 78rf[adrB] b,if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot x mem[adr2]);twert ( mem[adr2]); (then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 the adr1]vawerwesrwaerwearwerwerwerawerawerwarwearl);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe ni87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2 78 mem[ mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwer(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778ewrwerawer ewvtroiejwcro[iwehjnr[occwn3r[oweictweticwopjertijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);geroigtjer[ognifd;lindzgher[tjiserearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
x a;if opcode(m) = 101
then r b x;else r b x;
(x a, y b);z opcode(m);if z = 101then r x y;else r (x y);
Darmstadt University of Technology - 3 -
(if 78rf[adrB] b, x mem[adr2]);twert ( mem[adr2]); (if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe
erweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]); mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2 78 mem[adr1]vawerwesrwaerwearwerwerwerawerawerwarwearl);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778ewrwerawer ewvtroiejwcro[iwehjnr[occwn3r[oweictweticwopjertijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gergeroigtjer[ognifd;lindzgher[tjisereartoearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
tijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gergeroigtjer[ognifd;lindzgher[tjisereartoearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
(if 78r adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 f[adrB] b, x mem[adr2]);twert ( mem[adr2]); (if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe
erweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]); mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if i68i 778 then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);(if adrA adrBertetioerptkerotk8iperot
(if 78rf[adrB] b, x mem[adr2]);twert ( mem[adr2]); (if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2 78 mem[adr1]vawerwesrwaerwearwerwerwerawerawerwarwearl);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778ewrwerawer ewvtroiejwcro[iwehjnr[occwn3r[oweictweticwopjertijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gergeroigtjer[ognifd;lindzgher[tjisereartoearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
(if 78rf[adrB] b,if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot x mem[adr2]);twert ( mem[adr2]); (then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 the adr1]vawerwesrwaerwearwerwerwerawerawerwarwearl);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe ni87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2 78 mem[ mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwer(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778ewrwerawer ewvtroiejwcro[iwehjnr[occwn3r[oweictweticwopjertijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);geroigtjer[ognifd;lindzgher[tjiserearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
x a;if opcode(m) = 101
then r b x;else r b x;
ar
x
b
en_a en_rf
Darmstadt University of Technology - 4 -
r r+1;if m = 0
then r r+1;else r 000;
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm
Darmstadt University of Technology - 5 -
Verification Scope
automatic
interpreted
sequential
Verification
no significant user interaction
no insight into the verification process
automatic
Darmstadt University of Technology - 6 -
Verification Scope
automatic
interpreted
sequential
Verification
demonstrating the verification goal requires an interpretation of functions
not necessary for some problems where specialized approaches perform better
Darmstadt University of Technology - 7 -
Verification Scope
automatic
interpreted
sequential
Verification
not only logic verification
several control steps/cycles to demonstrate verification goal
different numbers of steps in specification and
implementation
Darmstadt University of Technology - 8 -
Outline introduction
essentials of our symbolicsimulation approach
example of gate-level verification
experimental results
application areas & conclusion
Darmstadt University of Technology - 9 -
techniques denoted “symbolic simulation“ or “symbolic evaluation” developed since the 1970s
the following four essentials distinguish our symbolic
simulation approach permit sequential verification at
different levels of abstraction
Essentials
Darmstadt University of Technology - 10 -
terms are never manipulated, e.g., by canonizing or rewriting them
1. Essential
ab ab=
a(bc) baSuppose
= 0c
Darmstadt University of Technology - 11 -
terms are never manipulated, e.g., by canonizing or rewriting them
1. Essential
relationships are notified atequivalence classes instead
a
c 0
a(bc) ba
a(bc) b
Darmstadt University of Technology - 12 -
ac+e+x[6:15]+y;
2. Essential
ac+e+x[6:15]+y+ac+e+x[6:15]+y;
Problem: term-size explosion possible if rewriting register with expression assigned to it
ac ac+e;bc x[6:15]+y;if ir=000111 then ac ac + bc ; res ac + ac ; else ...
Darmstadt University of Technology - 13 -
ac ac+e;bc x[6:15]+y;if ir=000111 then ac ac + bc ; res ac + ac ; else ...
2. Essential
ac1 ac+e;bc1 x[6:15]+y;if ir=000111 then ac2 ac1 + bc1; res1 ac2 + ac2; else ...
Problem: term-size explosion possible if rewriting register with expression assigned to it
Solution: several register assignments along a valid path are explicitly
distinguished
Darmstadt University of Technology - 14 -
ac ac+e;bc x[6:15]+y;if ir=000111 then ac ac + bc ; res ac + ac ; else ...
2. Essential
ac1 ac+e
ac1 ac+e;bc1 x[6:15]+y;if ir=000111 then ac2 ac1 + bc1; res1 ac2 + ac2; else ...
ac
ac2 ac1+bc1
Problem: term-size explosion possible if rewriting register with expression assigned to it
Solution: several register assignments along a valid path are explicitly
distinguished
Darmstadt University of Technology - 15 -
the verfication problem is not reduced to a single formula which is checked afterwards
3. Essential
VerificationProblem
Formulachecker
if z=101 then a¬bd elsif a¬bd then if(a+b)<(c+e)... .....
TRUE or FALSE
Darmstadt University of Technology - 16 -
3) a b
the verfication problem is not reduced to a single formula which is checked afterwards
simulation is guided along valid, i.e., logical consistent paths instead
3. Essential
...if a = b
then c y+5;else c a;
if a = cthen res ...;else res ...;
3 valid paths
1) a = b =c2) a = b c
Darmstadt University of Technology - 17 -
equivalence of subterms is sufficient in most cases to reveal equivalences of terms
4. Essential
aa(bc) ba
a(bc) b
c 0
Darmstadt University of Technology - 18 -
Challenges
equivalence detection of symbolic terms
consistent case splits during simulation must consider sequential behaviour avoid false paths
Darmstadt University of Technology - 19 -
Equivalence detection flexible use of an open library of different
equivalence detection techniquesduring symbolic simulation “on the fly” good compromise between
accuracy and speed not focus of this talk
decision diagram based techniques reveal “special” equivalences which occur seldom or are hard to detect
“Make the common case fast”
Darmstadt University of Technology - 20 -
r r+1;if m = 0
then r r+1;else r 000;
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm
Darmstadt University of Technology - 21 -
(if 78rf[adrB] b, x mem[adr2]);twert ( mem[adr2]); (if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2 78 mem[adr1]vawerwesrwaerwearwerwerwerawerawerwarwearl);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778ewrwerawer ewvtroiejwcro[iwehjnr[occwn3r[oweictweticwopjertijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gergeroigtjer[ognifd;lindzgher[tjisereartoearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
(if 78rf[adrB] b,if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot x mem[adr2]);twert ( mem[adr2]); (then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 the adr1]vawerwesrwaerwearwerwerwerawerawerwarwearl);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe ni87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2 78 mem[ mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwer(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778ewrwerawer ewvtroiejwcro[iwehjnr[occwn3r[oweictweticwopjertijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);geroigtjer[ognifd;lindzgher[tjiserearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
r r+1;if m = 0then r r +1;else r 000;
r1 r+1;if m1 = 0then r2 r1+1;else r2 000;
s
s ss
Darmstadt University of Technology - 22 -
(if 78rf[adrB] b, x mem[adr2]);twert ( mem[adr2]); (if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2 78 mem[adr1]vawerwesrwaerwearwerwerwerawerawerwarwearl);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778ewrwerawer ewvtroiejwcro[iwehjnr[occwn3r[oweictweticwopjertijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gergeroigtjer[ognifd;lindzgher[tjisereartoearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
(if 78rf[adrB] b,if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot x mem[adr2]);twert ( mem[adr2]); (then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 the adr1]vawerwesrwaerwearwerwerwerawerawerwarwearl);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe ni87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2 78 mem[ mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwer(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778ewrwerawer ewvtroiejwcro[iwehjnr[occwn3r[oweictweticwopjertijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);geroigtjer[ognifd;lindzgher[tjiserearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
r1 r+1;if m1 = 0then r2 r1+1;else r2 000;
r1 r+1;if m1 = 0then r2 r1+1;else r2 000;
s
s ss
r1 r+1
m1 0
r2 r1+1s ss
Darmstadt University of Technology - 23 -
duplicate according to number of
cycles (here: 2 cycles)
Gate-level design
describes only
one cycle...
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm
Darmstadt University of Technology - 24 -
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm
Break feed-back of registers...
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm
Darmstadt University of Technology - 25 -
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm
r[2]
r[1]
r[0]
Register-outputs of previous cycle are inputs of next cycle
ctrlctrl ctrl
Darmstadt University of Technology - 26 -
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm
r[2]
r[1]
r[0]
cycle 1 cycle 2initial
symbolicvalues
finalsymbolic
values
ctrlctrl ctrl
Darmstadt University of Technology - 27 -
Assumption about initialization of ctrl-register
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm1
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm
r[2]
r[1]
r[0]
ctrl ctrlctrl
Darmstadt University of Technology - 28 -
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm1
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm
r[2]
r[1]
r[0]
0
ctrl ctrlclk
ctrl ctrl
Assumption about initialization of ctrl-register
Darmstadt University of Technology - 29 -
Indexing the different register values
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm1
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm
r[2]
r[1]
r[0]
ctrl ctrl
0
clk
ctrl ctrl
Darmstadt University of Technology - 30 -
r2[2]
clk
&r2[1]&r2[0]&
r
&
&clk
ctrlm1
r1[2]
clk
&r1[1]&r1[0]&
r
&
&clk
ctrlm
r[2]
r[1]
r[0]
ctrl2 ctrl3
0
clk
ctrl ctrl1
Indexing the different register values
Darmstadt University of Technology - 31 -
1 ctrl1 nand m
r2[2]
clk
&r2[1]&r2[0]&
r
&
&clk
ctrlm1
r1[2]
clk
r1[1]
r1[0]
r
& clk
ctrlm
r[2]
r[1]
r[0]
ctrl2 ctrl3
0 ctrl1
ctrl10
0
1
clk
ctrl
&
&&&
Darmstadt University of Technology - 32 -
(not r[0])r1[0]
(ctrl1 nand m) and (not r[0])
r2[2]
clk
&r2[1]&r2[0]&
r
&
&clk
ctrlm1
r1[2]
r1[1]
r1[0]
& clk
ctrlm
r[2]
r[1]
r[0]
ctrl2 ctrl3
0 ctrl1
&clk
ctrl
r
clk
1
&&
&
Darmstadt University of Technology - 33 -
(r[1] xor r[0])r1[1]
(ctrl1 nand m) and (r[1] xor r[0])
r2[2]
clk
&r2[1]&r2[0]&
r
&
&clk
ctrlm1
r1[2]
r1[1]
r1[0]
&
&clk
ctrlm
r[2]
r[1]
r[0]
ctrl2 ctrl3
0
clk
ctrl ctrl1
r
clk
1
&&&
Darmstadt University of Technology - 34 -
r2[2]
clk
&r2[1]&r2[0]&
r
&
&clk
ctrlm1
r1[2]
clk
&r1[1]&r1[0]&
r
&
&clk
ctrlm
r[2]
r[1]
r[0]
ctrl2 ctrl3
0
clk
ctrl ctrl1
Darmstadt University of Technology - 35 -
(if 78rf[adrB] b, x mem[adr2]);twert ( mem[adr2]); (if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2 78 mem[adr1]vawerwesrwaerwearwerwerwerawerawerwarwearl);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778ewrwerawer ewvtroiejwcro[iwehjnr[occwn3r[oweictweticwopjertijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gergeroigtjer[ognifd;lindzgher[tjisereartoearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
(if 78rf[adrB] b,if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot x mem[adr2]);twert ( mem[adr2]); (then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 the adr1]vawerwesrwaerwearwerwerwerawerawerwarwearl);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe ni87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2 78 mem[ mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwer(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778ewrwerawer ewvtroiejwcro[iwehjnr[occwn3r[oweictweticwopjertijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);geroigtjer[ognifd;lindzgher[tjiserearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
r1 r+1;if m1 = 0then r2 r1+1;else r2 000;
s
s ss
r1 r+1
m1 0
r2 r1+1s ss
Darmstadt University of Technology - 36 -
r1 r+1s
r2[2]
clk
&r2[1]&r2[0]&
r
&
&clk
ctrlm1
r1[2]
clk
&r1[1]&r1[0]&
r
&
&clk
ctrlm
r[2]
r[1]
r[0]
ctrl2 ctrl3
0
clk
ctrl ctrl1
?
Darmstadt University of Technology - 37 -
Decision Diagram basedTechniques
reveal “special” equivalences which occur seldom or are hard to detect
build formula for equivalence use results of other equivalence detection
techniques “on the fly” information notified at equivalence classes
check formula by vectors of OBDDs
Darmstadt University of Technology - 38 -
Formula checkedin this example
r+1r1[2]
clk
&r1[1]&r1[0]&
r
&
&m
r[2]
r[1]
r[0]
0
clk
ctrl
Darmstadt University of Technology - 39 -
Formula checkedin this example
a+1
&a[2]a[1]
a[0]
Darmstadt University of Technology - 40 -
?r1 r+1s
r2[2]
clk
&r2[1]&r2[0]&
r
&
&clk
ctrlm1
r1[2]
clk
&r1[1]&r1[0]&
r
&
&clk
ctrlm
r[2]
r[1]
r[0]
ctrl2 ctrl3
0
clk
ctrl ctrl1
Darmstadt University of Technology - 41 -
r2[2]
clk
r2[1]
r2[0]
r
& clk
ctrlm1
r1[2]
clk
&r1[1]&r1[0]&
r
& clk
m
r[2]
r[1]
r[0]
ctrl2 ctrl3
0 ctrl10
clk
ctrl
&
1
ctrl1
&&&
0 &
Darmstadt University of Technology - 42 -
r2[2]
r2[1]
& clk
ctrlm1
r1[2]
clk
&r1[1]&
&
r
&
&clk
m
r[2]
r[1]
r[0]
ctrl2 ctrl3
0
clk
ctrl ctrl1
&
r1[0]
ctrl
r2[0]
1
&&&
r
clk
Darmstadt University of Technology - 43 -
(if 78rf[adrB] b, x mem[adr2]);twert ( mem[adr2]); (if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2 78 mem[adr1]vawerwesrwaerwearwerwerwerawerawerwarwearl);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778ewrwerawer ewvtroiejwcro[iwehjnr[occwn3r[oweictweticwopjertijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gergeroigtjer[ognifd;lindzgher[tjisereartoearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
(if 78rf[adrB] b,if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot x mem[adr2]);twert ( mem[adr2]); (then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 the adr1]vawerwesrwaerwearwerwerwerawerawerwarwearl);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe ni87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2 78 mem[ mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwer(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778ewrwerawer ewvtroiejwcro[iwehjnr[occwn3r[oweictweticwopjertijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);geroigtjer[ognifd;lindzgher[tjiserearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
r1 r+1;if m1 = 0then r2 r1+1;else r2 000;
s
s ss
r1 r+1
m1 0
r2 r1+1s ss
Darmstadt University of Technology - 44 -
r2 r1+1s s
r2[2]&r2[1]&r2[0]
&
&clk
ctrlm1
r1[2]
clk
&r1[1]&r1[0]&
r
&
&clk
ctrlm
r[2]
r[1]
r[0]
ctrl2 ctrl3
0
clk
ctrl ctrl1
?
r
clk
&
Darmstadt University of Technology - 45 -
r2[2]
clk
&r2[1]&r2[0]&
r
&
&clk
ctrlm1
r1[2]
clk
&r1[1]&r1[0]&
r
&
&clk
ctrlm
r[2]
r[1]
r[0]
ctrl2 ctrl3
0
clk
ctrl ctrl1
(r+1)+1
Darmstadt University of Technology - 46 -
r2[2]
clk
&r2[1]&r2[0]&
r
&
&clk
ctrlm1
r1[2]
clk
&r1[1]&r1[0]&
r
&
&clk
ctrlm
r[2]
r[1]
r[0]
ctrl2 ctrl3
0
clk
ctrl ctrl1
the equivalent termsare used as “cutpoints”
Darmstadt University of Technology - 47 -
r1 r+1;if m1 = 0then r2 r1+1;else r2 000;
s
s
s
s
r1 r+1;if m1 = 0then r2 r1+1;else r2 000;
s
s
s
s
r2[2]
clk
&r2[1]&r2[0]&
r
&
&clk
ctrlm1
ctrl2 ctrl3
the equivalent termsare used as “cutpoints”
r1[2]
r1[1]
r1[0]
use again information of equivalence classes to obtain simpler formula
Darmstadt University of Technology - 48 -
&a[2]a[1]
a[0]
a+1
Reuse hashed result no need to build OBDDs again
Darmstadt University of Technology - 49 -
?r2 r1+1s s
r2[2]&r2[1]&r2[0]
&
&clk
ctrlm1
r1[2]
clk
&r1[1]&r1[0]&
r
&
&clk
ctrlm
r[2]
r[1]
r[0]
ctrl2 ctrl3
0
clk
ctrl ctrl1
clk
&
r
Darmstadt University of Technology - 50 -
(if 78rf[adrB] b, x mem[adr2]);twert ( mem[adr2]); (if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2 78 mem[adr1]vawerwesrwaerwearwerwerwerawerawerwarwearl);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778ewrwerawer ewvtroiejwcro[iwehjnr[occwn3r[oweictweticwopjertijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gergeroigtjer[ognifd;lindzgher[tjisereartoearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
(if 78rf[adrB] b,if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 (if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR werwerweroewihgoerijhgbe mem[adr2]);twersfawetwerwerweroewihgoerijhgbe(if adrA adrBertetioerptkerotk8iperot x mem[adr2]);twert ( mem[adr2]); (then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778 the adr1]vawerwesrwaerwearwerwerwerawerawerwarwearl);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);werwerweoiruwepoir,pweiurcmpouopeiwurwrwerwerweirwerwereri we ewroiw weioruwerijw
oewriefwerwerwethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe ni87 i else zx+rf[adrR]);7i 7878 78then zval+rf[adrR]7 878 i78 i87 i else zx+rf[adrR]);7i 7878 (if adr1=adr2 78 mem[ mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);l);then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[wwerwerwerwaerwdr2]);wrwerwerl);erwrwerwer(if adr1=adr2etyer54 78768 7776 8676 i68i 778 then zval+rf[adrR ( mem[adr2]);twerweroewihg(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe(if adrA adrBertetioerptkerotk8iperot then rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr1]val);(if adr1=adr2etyer54 78768 7776 8676 i68i 778ewrwerawer ewvtroiejwcro[iwehjnr[occwn3r[oweictweticwopjertijeroginhreisgvbsdrpgvjnsdprigjzseriogjerogh;serozighzr;‘ongvosrzegmnseirogregoerijngerzos[goxdrijzdghnb;zdriozdjo‘gerwerwerwet5erioustgnfodsegkjerogtkjerogtkjerogtkmeorkegmrkhmgethen rf[adrA] a;erteroterj[o ermjgi7ethbe mem[adr2]);twertwerwerweroewihgoerijhgbe(if 78 mem[adr1]val);x mem[adr2]);(if adrA adrB then rf[adrA] a; mem[adr1]val); then zval+rf[adrR] else zx+rf[adrR]);mem[adr1]val);geroigtjer[ognifd;lindzgher[tjiserearjiopgb;zjndfl/gmnio;dlzkhrje;oyhinser[ohinmstophtrfshsrtyoeaijyeoritisoert
r1 r+1;if m1 = 0then r2 r1+1;else r2 000;
r1 r+1;if m1 = 0then r2 r1+1;else r2 000;
s
s ss
r1 r+1 m1 1
r2 0s
s
Other case ...
Darmstadt University of Technology - 51 -
&
ctrlm1
r1[2]
clk
&r1[1]&r1[0]&
r
& clk
m
r[2]
r[1]
r[0]
ctrl2 ctrl3
0 ctrl10
clk
ctrl
&
1
ctrl0
&&&
1 &
clk
r
clkr2[2]
r2[1]
r2[0]
Darmstadt University of Technology - 52 -
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm
datapath-operations are performed on separate blocks from standard libraries
Darmstadt University of Technology - 53 -
clk
&&&
r
&clk
ctrlm
INC
3
3
no decision diagrams required for symbolic simulation
datapath-operations are performed on separate blocks from standard libraries
use high-leveloperation “inc”
Darmstadt University of Technology - 54 -
r r+1;if m = 0
then r r+1;else r 000;
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm
cycle equivalent
Darmstadt University of Technology - 55 -
r[2]
clk
&r[1]&r[0]&
r
&
&clk
ctrlm
if m = 0then r r+2;else r 000;
NOTcycle equivalent
Darmstadt University of Technology - 56 -
Experimental Results
Verificationcheck number spec impl time
(1) RWA (one cycle) 1 1 -(2) RWA (one instruction) 3 3 -(3) MPA (with cycle-equiv.) 1 1 13(4) MPA (w/o cycle-equiv.) 92
cyclesdd-checks
1.7 s5.5 s74 s
786 s 8 10
Synthesis tool: Synopsys® Design Compiler™
Darmstadt University of Technology - 57 -
Application Area equivalence checking at different
levels of abstraction behavioral rtl structural rtl gate-level FMCAD’00, ASIAN’99, CHARME’99 et al
first application to property verification register binding verification C. Blank, Wave’2000
Darmstadt University of Technology - 58 -
Limitations
verification of finite sequences the maximum number of loop iterations
has to be known verification problem can be reduced for
many cyclic designs with infinite loops to
check of acyclic sequences
examples used in experiments still notnearly so complex as commercial designs
Darmstadt University of Technology - 59 -
Conclusion sequential verification of examples at
different levels of abstraction
flexible use of an open library of different equivalence detection techniques good compromise between
accuracy and speed
good debugging support
joint work withTIMA laboratory, Grenoble
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