Semiring-based constraint satisfaction and optimization
Journal of the ACM (JACM)
Handbook of graph grammars and computing by graph transformation: volume I. foundations
Handbook of graph grammars and computing by graph transformation: volume I. foundations
Model checking
Semiring-based constraint logic programming: syntax and semantics
ACM Transactions on Programming Languages and Systems (TOPLAS)
Introduction to Algorithms
Soft Constraint Logic Programming and Generalized Shortest Path Problems
Journal of Heuristics
Quantitative Temporal Reasoning
CAV '90 Proceedings of the 2nd International Workshop on Computer Aided Verification
A Modal Mu-Calculus for Durational Transition Systems
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Quantitative Analysis and Model Checking
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Service overlay networks: SLAs, QoS, and bandwidth provisioning
IEEE/ACM Transactions on Networking (TON)
Multi-valued symbolic model-checking
ACM Transactions on Software Engineering and Methodology (TOSEM)
Quantitative μ-calculus and CTL Based on Constraint Semirings
Electronic Notes in Theoretical Computer Science (ENTCS)
Verifying a Behavioural Logic for Graph Transformation Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
A temporal logic for Markov chains
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
A Logic for Application Level QoS
Electronic Notes in Theoretical Computer Science (ENTCS)
Exploiting the hierarchical structure of rule-based specifications for decision planning
FMOODS'10/FORTE'10 Proceedings of the 12th IFIP WG 6.1 international conference and 30th IFIP WG 6.1 international conference on Formal Techniques for Distributed Systems
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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 well-known temporal logics: CTL and the µ-calculus. Both extensions are defined over c-semirings, an algebraic structure that captures quantitative aspects like quality of service or soft constraints. Basically, a c-semiring 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 c-semiring, and show that the usual connection between CTL and µ-calculus does not hold in general. In addition, we reason about the complexity of computing the logics and illustrate some applications of our framework, including boolean model checking.