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Verifying quantitative properties using bound functions
 In CHARME: Correct Hardware Design and Verification Methods, LNCS 3725
, 2005
"... Abstract. We define and study a quantitative generalization of the traditional boolean framework of modelbased 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 propositi ..."
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Abstract. We define and study a quantitative generalization of the traditional boolean framework of modelbased 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 a 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 quantitativebound 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 lineartime, automatonbased view of quantitative verification, we present a corresponding branchingtime view based on a quantitativebound µcalculus, and we study the relationship, expressive power, and complexity of both views. 1
Reachability in Timed Counter Systems
, 2008
"... We introduce Timed Counter Systems, a new class of systems mixing clocks and counters. Such systems have an infinite state space, and their reachability problems are generally undecidable. By abstracting clock values with a Region Graph, we show the Counter Reachability Problem to be decidable for t ..."
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Cited by 1 (0 self)
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We introduce Timed Counter Systems, a new class of systems mixing clocks and counters. Such systems have an infinite state space, and their reachability problems are generally undecidable. By abstracting clock values with a Region Graph, we show the Counter Reachability Problem to be decidable for three subclasses: Timed VASS, Bounded Timed Counter
Systems, and ReversalBounded Timed Counter Systems.
"... We introduce Timed Counter Systems, a new class of systems mixing clocks and counters. Such systems have an infinite state space, and their reachability problems are generally undecidable. By abstracting clock values with a Region Graph, we show the Counter Reachability Problem to be decidable for t ..."
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We introduce Timed Counter Systems, a new class of systems mixing clocks and counters. Such systems have an infinite state space, and their reachability problems are generally undecidable. By abstracting clock values with a Region Graph, we show the Counter Reachability Problem to be decidable for three subclasses: Timed VASS, Bounded Timed Counter