TY - GEN

T1 - Verifying quantitative properties using bound functions

AU - Chakrabarti, Arindam

AU - Chatterjee, Krishnendu

AU - Henzinger, Thomas A.

AU - Kupferman, Orna

AU - Majumdar, Rupak

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33646435061&partnerID=8YFLogxK

U2 - 10.1007/11560548_7

DO - 10.1007/11560548_7

M3 - Conference contribution

AN - SCOPUS:33646435061

SN - 3540291059

SN - 9783540291053

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 50

EP - 64

BT - Correct Hardware Design and Verification Methods - 13th IFIP WG 10.5 Advanced Research Working Conference, CHARME 2005, Proceedings

T2 - 13th IFIP WG 10.5 Advanced Research Working Conference on Correct Hardware Design and Verification Methods, CHARME 2005

Y2 - 3 October 2005 through 6 October 2005

ER -