Certifying inexpressibility

Orna Kupferman, Salomon Sickert*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

Different classes of automata on infinite words have different expressive power. Deciding whether a given language L ⊆ Σω can be expressed by an automaton of a desired class can be reduced to deciding a game between Prover and Refuter: in each turn of the game, Refuter provides a letter in Σ, and Prover responds with an annotation of the current state of the run (for example, in the case of Büchi automata, whether the state is accepting or rejecting, and in the case of parity automata, what the color of the state is). Prover wins if the sequence of annotations she generates is correct: it is an accepting run iff the word generated by Refuter is in L. We show how a winning strategy for Refuter can serve as a simple and easy-to-understand certificate to inexpressibility, and how it induces additional forms of certificates. Our framework handles all classes of deterministic automata, including ones with structural restrictions like weak automata. In addition, it can be used for refuting separation of two languages by an automaton of the desired class, and for finding automata that approximate L and belong to the desired class.

Original languageAmerican English
Title of host publicationFoundations of Software Science and Computation Structures - 24th International Conference, FOSSACS 2021 Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021, Proceedings
EditorsStefan Kiefer, Christine Tasson
PublisherSpringer Science and Business Media Deutschland GmbH
Pages385-405
Number of pages21
ISBN (Print)9783030719944
DOIs
StatePublished - 2021
Event24th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2021 held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021 - Virtual, Online
Duration: 27 Mar 20211 Apr 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12650
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference24th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2021 held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021
CityVirtual, Online
Period27/03/211/04/21

Bibliographical note

Publisher Copyright:
© The Author(s) 2021.

Keywords

  • Automata on infinite words
  • Expressive power
  • Games

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