Monotonicity Characterizations of Regular Languages

Yoav Feinstein*, Orna Kupferman*

*Corresponding author for this work

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

Abstract

Each language L ? S induces an infinite sequence {Pr(L, n)}8n=1, where for all n = 1, the value Pr(L, n) ? [0, 1] is the probability of a word of length n to be in L, assuming a uniform distribution on the letters in S. Previous studies of {Pr(L, n)}8n=1 for a regular language L, concerned zero-one laws, density, and accumulation points. We study monotonicity of {Pr(L, n)}8n=1, possibly in the limit. We show that monotonicity may depend on the distribution of letters, study how operations on languages affect monotonicity, and characterize classes of languages for which the sequence is monotonic. We extend the study to languages L of infinite words, where we study the probability of lasso-shaped words to be in L and consider two definitions for Pr(L, n). The first refers to the probability of prefixes of length n to be extended to words in L, and the second to the probability of word w of length n to be such that w? is in L. Thus, in the second definition, monotonicity depends not only on the length of w, but also on the words being periodic.

Original languageAmerican English
Title of host publication43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2023
EditorsPatricia Bouyer, Srikanth Srinivasan, Srikanth Srinivasan
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages26:1-26:19
Number of pages19
ISBN (Electronic)9783959773041
DOIs
StatePublished - Dec 2023
Event43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2023 - Hyderabad, India
Duration: 18 Dec 202320 Dec 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume284
ISSN (Print)1868-8969

Conference

Conference43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2023
Country/TerritoryIndia
CityHyderabad
Period18/12/2320/12/23

Bibliographical note

Publisher Copyright:
© 2023 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

Keywords

  • Automata
  • Monotonicity
  • Probability
  • Regular Languages

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