TransducersTransducers

Jacob DisonJacob Dison

What is a transducer? What is a transducer?

• Defined as a device that converts Defined as a device that converts one form of energy to another. one form of energy to another.

• Examples: Motors, Speakers, Examples: Motors, Speakers, Microphones, Antennas, Light Bulbs, Microphones, Antennas, Light Bulbs, Potentiometer, Gauges…Potentiometer, Gauges…

• Essentially Sensors and Actuators Essentially Sensors and Actuators

Finite-State Transducers Finite-State Transducers

• Two tapes, one for input and one for Two tapes, one for input and one for output.output.

• Converts a input into an output. Converts a input into an output.

• Mealy and Moore machines. Mealy and Moore machines.

Moore MachineMoore Machine

• Invented by Edward F. Moore (1925 -Invented by Edward F. Moore (1925 -2003)2003)

• Wrote Gedanken-experiments on Wrote Gedanken-experiments on sequential machines (1956)sequential machines (1956)

• Associates an output with each state Associates an output with each state of the machine.of the machine.

Moore Machine Formal Moore Machine Formal Definition Definition

• ((KK, Σ, , Σ, OO, δ, δ, D,, D, ss, , AA,),)

• K = StatesK = States

• ΣΣ = Input = Input

• O = OutputO = Output

• s = Initial States = Initial State

• A = Final StateA = Final State

• δδ = Transition Function = Transition Function

• D = Output FunctionD = Output Function

Moore NotationMoore Notation

Stoplight Example Stoplight Example

Mealy MachineMealy Machine

• Invented by George H. Mealy in 1955Invented by George H. Mealy in 1955

• Associates outputs with transitions. Associates outputs with transitions.

Mealy Machine Formal Mealy Machine Formal Definition Definition

• ((KK, Σ, , Σ, OO, , ss, , AA, δ), δ)

• K = StatesK = States

• ΣΣ = Input = Input

• O = OutputO = Output

• s = Initial States = Initial State

• A = Final StateA = Final State

• δδ = Transition Function = Transition Function

Mealy Notation Mealy Notation

Barcodes!Barcodes!

Parity Bit Generator Parity Bit Generator

Bidirectional Transducers Bidirectional Transducers

• Works in both directionsWorks in both directions

• Example: Soundex System Example: Soundex System

• Input: KaylorInput: Kaylor

• Output: K460 Output: K460

• Kahler, Kaler, Kaylor, Keeler, Kellar, Kahler, Kaler, Kaylor, Keeler, Kellar, Kelleher, Keller, Kelliher, Kilroe, Kilroy, Kelleher, Keller, Kelliher, Kilroe, Kilroy, Koehler, Kohler, Koller, and Kyler.Koehler, Kohler, Koller, and Kyler.

Weighted Transducers Weighted Transducers

• In addition to inputs and outputs, In addition to inputs and outputs, associates a weight, which can be a associates a weight, which can be a number of things including time, number of things including time, probability, distance… etc. probability, distance… etc.

Directions Directions

Hidden Markov ModelsHidden Markov Models

• Nondeterministic Finite State Nondeterministic Finite State Transducer Transducer

• Machine is hidden, only outputs can Machine is hidden, only outputs can be observed. be observed.

HMMHMM

Questions?Questions?

References References

• Elaine Rich. Automata, Elaine Rich. Automata, Computability and Computability and Complexity: Theory and Applications.Complexity: Theory and Applications. Prentice Prentice Hall. 2008. 96-98.Hall. 2008. 96-98.

• Emmanuel Roche, Yves Schabes. “Deterministic Emmanuel Roche, Yves Schabes. “Deterministic part-of-speech tagging with finite-state part-of-speech tagging with finite-state transducerstransducers..”” Computational Linguistics Computational Linguistics, , 21(2):227-253, June 1995.21(2):227-253, June 1995.

• Cyril Allauzen, Mehryar Mohri. “Cyril Allauzen, Mehryar Mohri. “pp-Subsequentiable -Subsequentiable Transducers.” Transducers.” AT&T Labs – ResearchAT&T Labs – Research

• Mohri, Mehryar “Weighted Finite-State Transducer Mohri, Mehryar “Weighted Finite-State Transducer Algorithms An Overview” Algorithms An Overview” AT&T Labs – ResearchAT&T Labs – Research

References References

• Pradel, Michael. “Finite-State Pradel, Michael. “Finite-State Transducers.” Transducers.” Seminar on Natural Seminar on Natural Language Processing. Language Processing. July 6, 2007. July 6, 2007.

• Hsu, Chun-Nan., Chang, Chien-Chi. Finite-Hsu, Chun-Nan., Chang, Chien-Chi. Finite-State Transducers for Semi-Structured State Transducers for Semi-Structured Text Mining. Text Mining. Institute of Information Institute of Information ScienceScience

• Wagner, F. “StateWORKS: Moore or Mealy Wagner, F. “StateWORKS: Moore or Mealy model?.” model?.” StateWORKS.com. StateWORKS.com. April, 2005. April, 2005.