Closure under reversal of languages over infinite alphabets

Daniel Genkin; Michael Kaminski; Liat Peterfreund

doi:10.1007/978-3-319-90530-3_13

Closure under reversal of languages over infinite alphabets

Daniel Genkin, Michael Kaminski^*, Liat Peterfreund

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

It is shown that languages definable by weak pebble automata are not closed under reversal. For the proof, we establish a kind of periodicity of an automaton’s computation over a specific set of words. The periodicity is partly due to the finiteness of the automaton description and partly due to the word’s structure. Using such a periodicity we can find a word such that during the automaton’s run on it there are two different, yet indistinguishable, configurations. This enables us to remove a part of that word without affecting acceptance. Choosing an appropriate language leads us to the desired result.

Original language	English
Title of host publication	Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings
Editors	Vladimir V. Podolskii, Fedor V. Fomin
Publisher	Springer Verlag
Pages	145-156
Number of pages	12
ISBN (Print)	9783319905297
DOIs	https://doi.org/10.1007/978-3-319-90530-3_13
State	Published - 2018
Externally published	Yes
Event	13th International Computer Science Symposium in Russia, CSR 2018 - Moscow, Russian Federation Duration: 6 Jun 2018 → 10 Jun 2018

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10846 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	13th International Computer Science Symposium in Russia, CSR 2018
Country/Territory	Russian Federation
City	Moscow
Period	6/06/18 → 10/06/18

Bibliographical note

Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.

Keywords

Closure properties
Infinite alphabets
Reversal
Weak pebble automata

Access to Document

10.1007/978-3-319-90530-3_13

Cite this

Genkin, D., Kaminski, M., & Peterfreund, L. (2018). Closure under reversal of languages over infinite alphabets. In V. V. Podolskii, & F. V. Fomin (Eds.), Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings (pp. 145-156). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10846 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-90530-3_13

Genkin, Daniel ; Kaminski, Michael ; Peterfreund, Liat. / Closure under reversal of languages over infinite alphabets. Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings. editor / Vladimir V. Podolskii ; Fedor V. Fomin. Springer Verlag, 2018. pp. 145-156 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Genkin, D, Kaminski, M & Peterfreund, L 2018, Closure under reversal of languages over infinite alphabets. in VV Podolskii & FV Fomin (eds), Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10846 LNCS, Springer Verlag, pp. 145-156, 13th International Computer Science Symposium in Russia, CSR 2018, Moscow, Russian Federation, 6/06/18. https://doi.org/10.1007/978-3-319-90530-3_13

Closure under reversal of languages over infinite alphabets. / Genkin, Daniel; Kaminski, Michael; Peterfreund, Liat.
Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings. ed. / Vladimir V. Podolskii; Fedor V. Fomin. Springer Verlag, 2018. p. 145-156 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10846 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - It is shown that languages definable by weak pebble automata are not closed under reversal. For the proof, we establish a kind of periodicity of an automaton’s computation over a specific set of words. The periodicity is partly due to the finiteness of the automaton description and partly due to the word’s structure. Using such a periodicity we can find a word such that during the automaton’s run on it there are two different, yet indistinguishable, configurations. This enables us to remove a part of that word without affecting acceptance. Choosing an appropriate language leads us to the desired result.

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Genkin D, Kaminski M, Peterfreund L. Closure under reversal of languages over infinite alphabets. In Podolskii VV, Fomin FV, editors, Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings. Springer Verlag. 2018. p. 145-156. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-90530-3_13

Closure under reversal of languages over infinite alphabets

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