A multiparameter analysis of the boundedness problem for vector addition systems
Journal of Computer and System Sciences
Parametric real-time reasoning
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Model-checking in dense real-time
Information and Computation - Special issue: selections from 1990 IEEE symposium on logic in computer science
Symbolic model checking for real-time systems
Information and Computation
Information Processing Letters
Parametric timing analysis for real-time systems
Information and Computation
Parametric Analysis of Computer Systems
Formal Methods in System Design
Parametric Analysis of Computer Systems
AMAST '97 Proceedings of the 6th International Conference on Algebraic Methodology and Software Technology
Automata For Modeling Real-Time Systems
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Linear Parametric Model Checking of Timed Automata
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Parametric Quantitative Temporal Reasoning
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
An Inverse Method for Parametric Timed Automata
Electronic Notes in Theoretical Computer Science (ENTCS)
On minimal elements of upward-closed sets
Theoretical Computer Science
Computing minimal elements of upward-closed sets for Petri nets
ICATPN'07 Proceedings of the 28th international conference on Applications and theory of Petri nets and other models of concurrency
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We investigate the problem of characterizing the solution spaces for timed automata augmented by unknown timing parameters (called timing parameter automata (TPA)). The main contribution of this paper is that we identify three non-trivial subclasses of TPAs, namely, upper-bound, lower-bound and bipartite TPAs, and analyze how hard it is to characterize the solution space. As it turns out, we are able to give complexity bounds for the sizes of the minimal (resp., maximal) elements which completely characterize the upward-closed (resp., downward-closed) solution spaces of upper-bound (resp., lower-bound) TPAs. For bipartite TPAs, it is shown that their solution spaces are not semilinear in general. We also extend our analysis to TPAs equipped with counters without zero-test capabilities.