LluchLafuente, Alberto and Montanari, Ugo Quantitative mucalculus and CTL Based on Constraint Semirings. Electronic Notes in Theoretical Computer Science, 112. pp. 3759. ISSN 15710661 (2005)

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Abstract
Model checking and temporal logics are boolean. The answer to the model checking question does a system satisfy a property? is either true or false, and properties expressed in temporal logics are defined over boolean propositions. While this classic approach is enough to specify and verify boolean temporal properties, it does not allow to reason about quantitative aspects of systems. Some quantitative extensions of temporal logics has been already proposed, especially in the context of probabilistic systems. They allow to answer questions like with which probability does a system satisfy a property? We present a generalization of two wellknown temporal logics: CTL and the [mu]calculus. Both extensions are defined over csemirings, an algebraic structure that captures many problems and that has been proposed as a general framework for soft constraint satisfaction problems (CSP). Basically, a csemiring consists of a domain, an additive operation and a multiplicative operation, which satisfy some properties. We present the semantics of the extended logics over transition systems, where a formula is interpreted as a mapping from the set of states to the domain of the csemiring, and show that the usual connection between CTL and [mu]calculus does not hold in general. In addition, we reason about the feasibility of computing the logics and illustrate some applications of our framework, including boolean model checking.
Item Type:  Article 

Identification Number:  10.1016/j.entcs.2004.02.063 
Additional Information:  Proceedings of the Second Workshop on Quantitative Aspects of Programming Languages (QAPL 2004) 
Funders:  This work has been supported by the European Research Training Network SEGRAVIS. 
Uncontrolled Keywords:  Constraint Semirings; Constraints; Temporal Logics; Quantitative Model Checking 
Subjects:  Q Science > QA Mathematics > QA75 Electronic computers. Computer science 
Research Area:  Computer Science and Applications 
Depositing User:  Users 30 not found. 
Date Deposited:  24 Mar 2011 10:41 
Last Modified:  07 Oct 2014 14:51 
URI:  http://eprints.imtlucca.it/id/eprint/165 
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