Handbook of theoretical computer science (vol. B)
Parametric real-time reasoning
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Minimum and maximum delay problems in real-time systems
Formal Methods in System Design - Special issue on computer-aided verification: special methods I
Model-checking in dense real-time
Information and Computation - Special issue: selections from 1990 IEEE symposium on logic in computer science
The benefits of relaxing punctuality
Journal of the ACM (JACM)
Parametric timing analysis for real-time systems
Information and Computation
Parametric temporal logic for “model measuring”
ACM Transactions on Computational Logic (TOCL)
Selective Quantitative Analysis and Interval Model Checking: Verifying Different Facets of a System
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Parametric Quantitative Temporal Reasoning
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Durations and parametric model-checking in timed automata
ACM Transactions on Computational Logic (TOCL)
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Timed verification of the generic architecture of a memory circuit using parametric timed automata
Formal Methods in System Design
Formal Methods in System Design
Decision problems for lower/upper bound parametric timed automata
Formal Methods in System Design
Parametric identification of temporal properties
RV'11 Proceedings of the Second international conference on Runtime verification
Optimal bounds in parametric LTL games
Theoretical Computer Science
Automata-theoretic decision of timed games
Theoretical Computer Science
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We study an extension of the logic MITL with parametric constants. In particular, we define a logic, denoted PMITL (parametric MITL), where the subscripts of the temporal operators are intervals with possibly a parametric endpoint. We consider typical decision problems, such as emptiness and universality of the set of parameter valuations under which a given parametric formula is satisfiable, or whether a given parametric timed automaton is a model of a given parametric formula. We show that when each parameter is used with a fixed polarity and only parameter valuations which evaluate parametric intervals to non-singular time intervals are taken into consideration, then the considered problems are decidable and Expspace-complete. We also investigate the computational complexity of these problems for natural fragments of PMITL, and show that in meaningful fragments of the logic they are Pspace-complete. Finally, we discuss other natural parameterizations of MITL, which indeed lead to undecidability.