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 1 / 10

Outline 2 / 10

Regular Relations Closure Properties Regular Relations are closed under the following operations ◮ Concatenation 3 / 10

Regular Relations Closure Properties Regular Relations are closed under the following operations ◮ Concatenation ◮ Union 3 / 10

Regular Relations Closure Properties Regular Relations are closed under the following operations ◮ Concatenation ◮ Union ◮ Kleene Star 3 / 10

Regular Relations Closure Properties Regular Relations are closed under the following operations ◮ Concatenation ◮ Union ◮ Kleene Star ◮ Composition 3 / 10

Regular Relations Closure Properties Unlike Regular Languages regular relations are not closed under the following operations: ◮ Intersection 4 / 10

Regular Relations Closure Properties Unlike Regular Languages regular relations are not closed under the following operations: ◮ Intersection ◮ Complementation 4 / 10

Regular Relations Closure Properties Unlike Regular Languages regular relations are not closed under the following operations: ◮ Intersection ◮ Complementation ◮ Difference 4 / 10

Regular Relations 5 / 10

Regular Relations Therefore, in the Xerox implementation, general intersection does not work! Example: 6 / 10

Regular Relations Therefore, in the Xerox implementation, general intersection does not work! Example: 7 / 10

Regular Relations However: ”Koskenniemi’s 2 levels” and corresponding implementation in xfst ? 8 / 10

Regular Relations However: ”Koskenniemi’s 2 levels” and corresponding implementation in xfst ? Solution Syntax of replace rules: 9 / 10

Regular Relations However: ”Koskenniemi’s 2 levels” and corresponding implementation in xfst ? Solution Syntax of replace rules: 10 / 10