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
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(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: 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.
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•
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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,
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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.