Transducers
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Transducers. Jacob Dison. What is a transducer? . Defined as a device that converts one form of energy to another. Examples: Motors, Speakers, Microphones, Antennas, Light Bulbs, Potentiometer, Gauges… Essentially Sensors and Actuators . Finite-State Transducers .

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Transducers

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Transducers

Transducers

Jacob Dison


What is a transducer

What is a transducer?

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

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

  • Essentially Sensors and Actuators


Finite state transducers

Finite-State Transducers

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

  • Converts a input into an output.

  • Mealy and Moore machines.


Moore machine

Moore Machine

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

  • Wrote Gedanken-experiments on sequential machines (1956)

  • Associates an output with each state of the machine.


Moore machine formal definition

Moore Machine Formal Definition

  • (K, Σ, O, δ, D,s, A,)

  • K = States

  • Σ = Input

  • O = Output

  • s = Initial State

  • A = Final State

  • δ = Transition Function

  • D = Output Function


Moore notation

Moore Notation


Stoplight example

Stoplight Example


Mealy machine

Mealy Machine

  • Invented by George H. Mealy in 1955

  • Associates outputs with transitions.


Mealy machine formal definition

Mealy Machine Formal Definition

  • (K, Σ, O, s, A, δ)

  • K = States

  • Σ = Input

  • O = Output

  • s = Initial State

  • A = Final State

  • δ = Transition Function


Mealy notation

Mealy Notation


Barcodes

Barcodes!


Parity bit generator

Parity Bit Generator


Bidirectional transducers

Bidirectional Transducers

  • Works in both directions

  • Example: Soundex System

  • Input: Kaylor

  • Output: K460

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


Weighted transducers

Weighted Transducers

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


Directions

Directions


Hidden markov models

Hidden Markov Models

  • Nondeterministic Finite State Transducer

  • Machine is hidden, only outputs can be observed.


Transducers

HMM


Questions

Questions?


References

References

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

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

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

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


References1

References

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

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

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


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