Verifying quantitative properties using bound functions

Arindam Chakrabarti*, Krishnendu Chatterjee, Thomas A. Henzinger, Orna Kupferman, Rupak Majumdar

*Corresponding author for this work

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

26 Scopus citations


We define and study a quantitative generalization of the traditional boolean framework of model-based specification and verification. In our setting, propositions have integer values at states, and properties have integer values on traces. For example, the value of a quantitative proposition at a state may represent power consumed at the state, and the value of a quantitative property on a trace may represent energy used along the trace. The value of a quantitative property at &. state, then, is the maximum (or minimum) value achievable over all possible traces from the state. In this framework, model checking can be used to compute, for example, the minimum battery capacity necessary for achieving a given objective, or the maximal achievable lifetime of a system with a given initial battery capacity. In the case of open systems, these problems require the solution of games with integer values. Quantitative model checking and game solving is undecidable, except if bounds on the computation can be found. Indeed, many interesting quantitative properties, like minimal necessary battery capacity and maximal achievable lifetime, can be naturally specified by quantitative-bound automata, which are finite automata with integer registers whose analysis is constrained by a bound function f that maps each system K to an integer f(K). Along with the linear-time, automaton-based view of quantitative verification, we present a corresponding branching-time view based on a quantitative-bound μ-calculus, and we study the relationship, expressive power, and complexity of both views.

Original languageAmerican English
Title of host publicationCorrect Hardware Design and Verification Methods - 13th IFIP WG 10.5 Advanced Research Working Conference, CHARME 2005, Proceedings
Number of pages15
StatePublished - 2005
Event13th IFIP WG 10.5 Advanced Research Working Conference on Correct Hardware Design and Verification Methods, CHARME 2005 - Saarbruecken, Germany
Duration: 3 Oct 20056 Oct 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3725 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference13th IFIP WG 10.5 Advanced Research Working Conference on Correct Hardware Design and Verification Methods, CHARME 2005


Dive into the research topics of 'Verifying quantitative properties using bound functions'. Together they form a unique fingerprint.

Cite this