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Verifying temporal properties of processes
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Symbolic model checking for real-time systems
Information and Computation
Model checking and abstraction
ACM Transactions on Programming Languages and Systems (TOPLAS)
The algebra of timed processes, ATP: theory and application
Information and Computation
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ACM Transactions on Programming Languages and Systems (TOPLAS)
Selective mu-calculus and formula-based equivalence of transition systems
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Proceedings of the Real-Time: Theory in Practice, REX Workshop
Selective µ-calculus: New Modal Operators for Proving Properties on Reduced Transition Systems
FORTE X / PSTV XVII '97 Proceedings of the IFIP TC6 WG6.1 Joint International Conference on Formal Description Techniques for Distributed Systems and Communication Protocols (FORTE X) and Protocol Specification, Testing and Verification (PSTV XVII)
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When verifying concurrent systems described by transition systems, state explosion is one of the most serious problems. If quantitative temporal information (expressed by clock ticks) is considered, state explosion is even more serious. We present a notion of abstraction of transition systems, where the abstraction is driven by the formulae of a quantitative temporal logic, called qu-mu-calculus, defined in the paper. The abstraction is based on a notion of bisimulation equivalence, called 〈ρ, n〉-equivalence, where ρ is a set of actions and n is a natural number. It is proved that two transition systems are 〈ρ, n〉-equivalent iff they give the same truth value to all qu-mu-calculus formulae such that the actions occurring in the modal operators are contained in ρ, and with time constraints whose values are less than or equal to n. We present a non-standard (abstract) semantics for a timed process algebra able to produce reduced transition systems for checking formulae. The abstract semantics, parametric with respect to a set ρ of actions and a natural number n, produces a reduced transition system 〈ρ, n〉-equivalent to the standard one. A transformational method is also defined, by means of which it is possible to syntactically transform a program into a smaller one, still preserving 〈ρ, n〉-equivalence.