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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

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

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

- (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

Mealy Machine

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

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

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

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

Hidden Markov Models

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

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

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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