1. Transducers Jacob Dison

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

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

4. Moore Machine Invented by Edward F. Moore (1925 - 2003) Invented by Edward F. Moore (1925 - 2003) Wrote Gedanken-experiments on sequential machines (1956) Wrote Gedanken-experiments on sequential machines (1956) Associates an output with each state of the machine. Associates an output with each state of the machine.

5. Moore Machine Formal Definition (K, Σ, O, δ, D, s, A,) (K, Σ, O, δ, D, s, A,) K = States K = States Σ = Input Σ = Input O = Output O = Output s = Initial State s = Initial State A = Final State A = Final State δ = Transition Function δ = Transition Function D = Output Function D = Output Function

6. Moore Notation

7. Stoplight Example

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

9. Mealy Machine Formal Definition (K, Σ, O, s, A, δ) (K, Σ, O, s, A, δ) K = States K = States Σ = Input Σ = Input O = Output O = Output s = Initial State s = Initial State A = Final State A = Final State δ = Transition Function δ = Transition Function

10. Mealy Notation

11. Barcodes!

12. Parity Bit Generator

13. Bidirectional Transducers Works in both directions Works in both directions Example: Soundex System Example: Soundex System Input: Kaylor Input: Kaylor Output: K460 Output: K460 Kahler, Kaler, Kaylor, Keeler, Kellar, Kelleher, Keller, Kelliher, Kilroe, Kilroy, Koehler, Kohler, Koller, and Kyler. 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. 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 Nondeterministic Finite State Transducer Machine is hidden, only outputs can be observed. 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. 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. 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 Cyril Allauzen, Mehryar Mohri. “p-Subsequentiable Transducers.” AT&T Labs – Research Mohri, Mehryar “Weighted Finite-State Transducer Algorithms An Overview” 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. 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 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. Wagner, F. “StateWORKS: Moore or Mealy model?.” StateWORKS.com. April, 2005.