Temporal specifications with accumulative values

Udi Boker*, Krishnendu Chatterjee, Thomas A. Henzinger, Orna Kupferman

*Corresponding author for this work

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

52 Scopus citations

Abstract

There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications. In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point of time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire computation. We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accumulation assertions, result in temporal logics whose model-checking problem is decidable. The extended logics allow to significantly extend the currently known energy and mean-payoff objectives. Moreover, the prefix-accumulation assertions may be refined with "controlled-accumulation", allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefix-accumulation assertions permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, and in particular CTL and LTL, makes the problem undecidable.

Original languageAmerican English
Title of host publicationProceedings - 26th Annual IEEE Symposium on Logic in Computer Science, LICS 2011
Pages43-52
Number of pages10
DOIs
StatePublished - 2011
Event26th Annual IEEE Symposium on Logic in Computer Science, LICS 2011 - Toronto, ON, Canada
Duration: 21 Jun 201124 Jun 2011

Publication series

NameProceedings - Symposium on Logic in Computer Science
ISSN (Print)1043-6871

Conference

Conference26th Annual IEEE Symposium on Logic in Computer Science, LICS 2011
Country/TerritoryCanada
CityToronto, ON
Period21/06/1124/06/11

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