Applications in finite state automata Completeness of Regular - - PowerPoint PPT Presentation

Applications in finite state automata

Completeness of Regular Relations Kurt Eberle

kurt.eberle@uni-tuebingen.de

(includes material from Thomas Hanneforth and Eric Gribkoff)

December 15, 2016

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Outline

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Regular Relations

Closure Properties

Regular Relations are closed under the following operations

◮ Concatenation

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Regular Relations

Closure Properties

Regular Relations are closed under the following operations

◮ Concatenation ◮ Union

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Regular Relations

Closure Properties

Regular Relations are closed under the following operations

◮ Concatenation ◮ Union ◮ Kleene Star

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Regular Relations

Closure Properties

Regular Relations are closed under the following operations

◮ Concatenation ◮ Union ◮ Kleene Star ◮ Composition

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Regular Relations

Closure Properties

Unlike Regular Languages regular relations are not closed under the following operations:

◮ Intersection

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Regular Relations

Closure Properties

Unlike Regular Languages regular relations are not closed under the following operations:

◮ Intersection ◮ Complementation

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Regular Relations

Closure Properties

Unlike Regular Languages regular relations are not closed under the following operations:

◮ Intersection ◮ Complementation ◮ Difference

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Regular Relations

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Regular Relations

Therefore, in the Xerox implementation, general intersection does not work! Example:

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Regular Relations

Therefore, in the Xerox implementation, general intersection does not work! Example:

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Regular Relations

However: ”Koskenniemi’s 2 levels” and corresponding implementation in xfst ?

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Regular Relations

However: ”Koskenniemi’s 2 levels” and corresponding implementation in xfst ? Solution Syntax of replace rules:

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Regular Relations

However: ”Koskenniemi’s 2 levels” and corresponding implementation in xfst ? Solution Syntax of replace rules:

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