Transducers Jacob Dison What is a transducer Defined

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

Moore Notation

Stoplight Example

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

Mealy Notation

Barcodes!

Parity Bit Generator

Bidirectional Transducers • Works in both directions • Example: Soundex System • Input: Kaylor • Output: K 460 • Kahler, Kaylor, Keeler, Kellar, Kelleher, Kelliher, Kilroe, Kilroy, Koehler, 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.

Directions

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

HMM

Questions?

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. “State. WORKS: Moore or Mealy model? . ” State. WORKS. com. April, 2005.