Weighted safety

Sigal Weiner, Matan Hasson, Orna Kupferman, Eyal Pery, Zohar Shevach

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

5 Scopus citations

Abstract

Safety properties, which assert that the system always stays within some allowed region, have been extensively studied and used. In the last years, we see more and more research on quantitative formal methods, where systems and specifications are weighted. We introduce and study safety in the weighted setting. For a value v ∈ ℚ, we say that a weighted language L : ∑* → ℚ is v-safe if every word with cost at least v has a prefix all whose extensions have cost at least v. The language L is then weighted safe if L is v-safe for some v. Given a regular weighted language L, we study the set of values v ∈ ℚ for which L is v-safe. We show that this set need not be closed upwards or downwards and we relate the v-safety of L with the safety of the (Boolean) language of words whose cost in L is at most v. We show that the latter need not be regular but is always context free. Given a deterministic weighted automaton A, we relate the safety of L(A) with the structure of A, and we study the problem of deciding whether L(A) is v-safe for a given v. We also study the weighted safety of L(A) and provide bounds on the minimal value |v| for which a weighted language L(A) is v-safe.

Original languageAmerican English
Title of host publicationAutomated Technology for Verification and Analysis - 11th International Symposium, ATVA 2013, Proceedings
Pages133-147
Number of pages15
DOIs
StatePublished - 2013
Event11th International Symposium on Automated Technology for Verification and Analysis, ATVA 2013 - Hanoi, Viet Nam
Duration: 15 Oct 201318 Oct 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8172 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th International Symposium on Automated Technology for Verification and Analysis, ATVA 2013
Country/TerritoryViet Nam
CityHanoi
Period15/10/1318/10/13

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