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Transducers

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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  1. Transducers Jacob Dison

  2. 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

  3. Finite-State Transducers • Two tapes, one for input and one for output. • Converts a input into an output. • Mealy and Moore machines.

  4. 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.

  5. 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

  6. Moore Notation

  7. Stoplight Example

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

  9. 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

  10. Mealy Notation

  11. Barcodes!

  12. Parity Bit Generator

  13. 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.

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

  15. Directions

  16. Hidden Markov Models • Nondeterministic Finite State Transducer • Machine is hidden, only outputs can be observed.

  17. HMM

  18. Questions?

  19. 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

  20. 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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