Transducers

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Transducers

• Jacob Dison

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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

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Finite-State Transducers

• Two tapes, one for input and one for output.
• Converts a input into an output.
• Mealy and Moore machines.

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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.

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Moore Machine Formal Definition

• (K, S, O, d, D, s, A,)
• K States
• S Input
• O Output
• s Initial State
• A Final State
• d Transition Function
• D Output Function

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Moore Notation
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Stoplight Example
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Mealy Machine

• Invented by George H. Mealy in 1955
• Associates outputs with transitions.

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Mealy Machine Formal Definition

• (K, S, O, s, A, d)
• K States
• S Input
• O Output
• s Initial State
• A Final State
• d Transition Function

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Mealy Notation
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Barcodes!
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Parity Bit Generator
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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.

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Weighted Transducers

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

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Directions
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Hidden Markov Models

• Nondeterministic Finite State Transducer
• Machine is hidden, only outputs can be observed.

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HMM
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Questions?
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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. ATT Labs Research
• Mohri, Mehryar Weighted Finite-State Transducer
  Algorithms An Overview ATT Labs Research

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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.