Spanning the spectrum from safety to liveness

Rachel Faran*, Orna Kupferman

*Corresponding author for this work

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

3 Scopus citations

Abstract

Of special interest in formal verification are safety specifications, which assert that the system stays within some allowed region, in which nothing “bad” happens. Equivalently, a computation violates a safety specification if it has a “bad prefix” – a prefix all whose extensions violate the specification. The theoretical properties of safety specifications as well as their practical advantages with respect to general specifications have been widely studied. Safety is binary: a specification is either safety or not safety. We introduce a quantitative measure for safety. Intuitively, the safety level of a language L measures the fraction of words not in L that have a bad prefix. In particular, a safety language has safety level 1 and a liveness language has safety level 0. Thus, our study spans the spectrum between traditional safety and liveness. The formal definition of safety level is based on probability and measures the probability of a random word not in L to have a bad prefix. We study the problem of finding the safety level of languages given by means of deterministic and nondeterministic automata as well as LTL formulas, and the problem of deciding their membership in specific classes along the spectrum (safety, almost-safety, fraction-safety, etc.). We also study properties of the different classes and the structure of deterministic automata for them.

Original languageAmerican English
Title of host publicationAutomated Technology for Verification and Analysis - 13th International Symposium, ATVA 2015, Proceedings
EditorsBernd Finkbeiner, Geguang Pu, Lijun Zhang
PublisherSpringer Verlag
Pages183-200
Number of pages18
ISBN (Print)9783319249520
DOIs
StatePublished - 2015
Event13th International Symposium on Automated Technology for Verification and Analysis, ATVA 2015 - Shanghai, China
Duration: 12 Oct 201515 Oct 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9364
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference13th International Symposium on Automated Technology for Verification and Analysis, ATVA 2015
Country/TerritoryChina
CityShanghai
Period12/10/1515/10/15

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2015.

Fingerprint

Dive into the research topics of 'Spanning the spectrum from safety to liveness'. Together they form a unique fingerprint.

Cite this