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Ch1-Finite Automata & Regular Languages

Ch1-Finite Automata & Regular Languages - Digital...

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Digital State Machines Finite Automata & Regular  Languages
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2/11/12 Veton K ë puska 2 Chapter Outline u Introduction u Finite-State Automata u Regular Languages and Finite-State Automata u Summary
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2/11/12 Veton K ë puska 3 Introduction:  Finite State Automata u Finite-state automaton is one of the most significant tools of  computational linguistics. Its variations: n Finite-state transducers n Hidden Markov Models, and n N-gram grammars  Important components of the Speech Recognition and Synthesis, spell-checking, and  information-extraction applications. u The FSA theory was designed in the beginning of computer science as a  model of abstract computing machines pioneered by the work of Allan  Turing. n FSA’s are devices that accept-recognize or reject an input stream of characters. n FSA’s are very efficient in term of speed and memory  n The most frequent usage of Finite-State Automata is searching words or phrases. n Additional uses in application areas such as: u Morphological parsing, u Parts of speech annotation, and  u Speech Processing and Recognition.
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A Simple Example of  Finite State Automata q 0 Start q 1 a b q 2 c u This FSA accepts (recognizes) or generates  strings like: n ac n abc n abbc n abbbc, n abbbbbbbbbbc, etc. 2/11/12 Veton K ë puska 4
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State Transition Table of a Finite  State Automata q 0 Start q 1 a b q 2 c u State Transition Table of the FSA above 2/11/12 Veton K ë puska 5 Input  State a b c q0 q1 ˘ ˘ q1 ˘ q1 q 2 q2 ˘ ˘ ˘
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Example of Finite State Automata u An automaton accepts an input string in the  following way: n Starts in initial state, n Follows a transition where the arc character matches  the first character of the string, n Consumes the corresponding string character, n Reaches the destination state, n It makes next transition based on the current input  string,  n Ends up in one of the final states when there is no  characters left in the input.
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Introduction:  D-FSA vs. ND-FSA u Adding non-determinism to FSA will not allow us define any  language that can not be defined by deterministic FSAs. u Why then bother with ND-FSAs: n It turns out that there can be substantial efficiency in describing an  application using ND-FSAs. n ND-FSAs allows us to program solutions to problems using a higher-level  language. n This program then is compiled, by the algorithm (that we will learn in this  chapter), into a deterministic FSA that can be executed on a conventional  computer.
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