TY - GEN

T1 - Monotonicity Characterizations of Regular Languages

AU - Feinstein, Yoav

AU - Kupferman, Orna

N1 - Publisher Copyright: © 2023 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

PY - 2023/12

Y1 - 2023/12

N2 - 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.

AB - 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.

KW - Automata

KW - Monotonicity

KW - Probability

KW - Regular Languages

UR - http://www.scopus.com/inward/record.url?scp=85180736138&partnerID=8YFLogxK

U2 - https://doi.org/10.4230/LIPIcs.FSTTCS.2023.26

DO - https://doi.org/10.4230/LIPIcs.FSTTCS.2023.26

M3 - Conference contribution

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 26:1-26:19

BT - 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2023

A2 - Bouyer, Patricia

A2 - Srinivasan, Srikanth

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2023

Y2 - 18 December 2023 through 20 December 2023

ER -