transducers jacob dison. what is a transducer? defined as a device that converts one form of energy...
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TransducersTransducers
Jacob DisonJacob Dison
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What is a transducer? What is a transducer?
• Defined as a device that converts Defined as a device that converts one form of energy to another. one form of energy to another.
• Examples: Motors, Speakers, Examples: Motors, Speakers, Microphones, Antennas, Light Bulbs, Microphones, Antennas, Light Bulbs, Potentiometer, Gauges…Potentiometer, Gauges…
• Essentially Sensors and Actuators Essentially Sensors and Actuators
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Finite-State Transducers Finite-State Transducers
• Two tapes, one for input and one for Two tapes, one for input and one for output.output.
• Converts a input into an output. Converts a input into an output.
• Mealy and Moore machines. Mealy and Moore machines.
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Moore MachineMoore Machine
• Invented by Edward F. Moore (1925 -Invented by Edward F. Moore (1925 -2003)2003)
• Wrote Gedanken-experiments on Wrote Gedanken-experiments on sequential machines (1956)sequential machines (1956)
• Associates an output with each state Associates an output with each state of the machine.of the machine.
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Moore Machine Formal Moore Machine Formal Definition Definition
• ((KK, Σ, , Σ, OO, δ, δ, D,, D, ss, , AA,),)
• K = StatesK = States
• ΣΣ = Input = Input
• O = OutputO = Output
• s = Initial States = Initial State
• A = Final StateA = Final State
• δδ = Transition Function = Transition Function
• D = Output FunctionD = Output Function
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Moore NotationMoore Notation
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Stoplight Example Stoplight Example
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Mealy MachineMealy Machine
• Invented by George H. Mealy in 1955Invented by George H. Mealy in 1955
• Associates outputs with transitions. Associates outputs with transitions.
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Mealy Machine Formal Mealy Machine Formal Definition Definition
• ((KK, Σ, , Σ, OO, , ss, , AA, δ), δ)
• K = StatesK = States
• ΣΣ = Input = Input
• O = OutputO = Output
• s = Initial States = Initial State
• A = Final StateA = Final State
• δδ = Transition Function = Transition Function
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Mealy Notation Mealy Notation
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Barcodes!Barcodes!
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Parity Bit Generator Parity Bit Generator
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Bidirectional Transducers Bidirectional Transducers
• Works in both directionsWorks in both directions
• Example: Soundex System Example: Soundex System
• Input: KaylorInput: Kaylor
• Output: K460 Output: K460
• Kahler, Kaler, Kaylor, Keeler, Kellar, Kahler, Kaler, Kaylor, Keeler, Kellar, Kelleher, Keller, Kelliher, Kilroe, Kilroy, Kelleher, Keller, Kelliher, Kilroe, Kilroy, Koehler, Kohler, Koller, and Kyler.Koehler, Kohler, Koller, and Kyler.
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Weighted Transducers Weighted Transducers
• In addition to inputs and outputs, In addition to inputs and outputs, associates a weight, which can be a associates a weight, which can be a number of things including time, number of things including time, probability, distance… etc. probability, distance… etc.
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Directions Directions
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Hidden Markov ModelsHidden Markov Models
• Nondeterministic Finite State Nondeterministic Finite State Transducer Transducer
• Machine is hidden, only outputs can Machine is hidden, only outputs can be observed. be observed.
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HMMHMM
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Questions?Questions?
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References References
• Elaine Rich. Automata, Elaine Rich. Automata, Computability and Computability and Complexity: Theory and Applications.Complexity: Theory and Applications. Prentice Prentice Hall. 2008. 96-98.Hall. 2008. 96-98.
• Emmanuel Roche, Yves Schabes. “Deterministic Emmanuel Roche, Yves Schabes. “Deterministic part-of-speech tagging with finite-state part-of-speech tagging with finite-state transducerstransducers..”” Computational Linguistics Computational Linguistics, , 21(2):227-253, June 1995.21(2):227-253, June 1995.
• Cyril Allauzen, Mehryar Mohri. “Cyril Allauzen, Mehryar Mohri. “pp-Subsequentiable -Subsequentiable Transducers.” Transducers.” AT&T Labs – ResearchAT&T Labs – Research
• Mohri, Mehryar “Weighted Finite-State Transducer Mohri, Mehryar “Weighted Finite-State Transducer Algorithms An Overview” Algorithms An Overview” AT&T Labs – ResearchAT&T Labs – Research
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References References
• Pradel, Michael. “Finite-State Pradel, Michael. “Finite-State Transducers.” Transducers.” Seminar on Natural Seminar on Natural Language Processing. Language Processing. July 6, 2007. July 6, 2007.
• Hsu, Chun-Nan., Chang, Chien-Chi. Finite-Hsu, Chun-Nan., Chang, Chien-Chi. Finite-State Transducers for Semi-Structured State Transducers for Semi-Structured Text Mining. Text Mining. Institute of Information Institute of Information ScienceScience
• Wagner, F. “StateWORKS: Moore or Mealy Wagner, F. “StateWORKS: Moore or Mealy model?.” model?.” StateWORKS.com. StateWORKS.com. April, 2005. April, 2005.