What’s decidable about parametric timed automata?

Parametric timed automata (PTAs) are a powerful formalism to reason, simulate and formally verify critical real-time systems. After 25 years of research on PTAs, it is now well understood that any non-trivial problem studied is undecidable for general PTAs. We provide here a survey of decision and c...

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Bibliographic Details
Published in:International journal on software tools for technology transfer Vol. 21; no. 2; pp. 203 - 219
Main Author: André, Étienne
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2019
Springer Nature B.V
Springer Verlag
Subjects:
Clocks
Computer Science
Computer simulation
Formal Languages and Automata Theory
Formalism
Logic in Computer Science
Lower bounds
Parameters
Regular Paper
Software Engineering
Software Engineering/Programming and Operating Systems
Theory of Computation
Parametric timed model checking
L/U-PTAs
Hybrid automata
Decidability
Parameter synthesis
Decision problems
hybrid systems
Parametric timed automata
Model checking
Parametric model checking
ISSN:1433-2779, 1433-2787
Online Access:Get full text
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Summary:Parametric timed automata (PTAs) are a powerful formalism to reason, simulate and formally verify critical real-time systems. After 25 years of research on PTAs, it is now well understood that any non-trivial problem studied is undecidable for general PTAs. We provide here a survey of decision and computation problems for PTAs. On the one hand, bounding time, bounding the number of parameters or the domain of the parameters does not (in general) lead to any decidability. On the other hand, restricting the number of clocks, the use of clocks (compared or not with the parameters), and the use of parameters (e. g., used only as upper or lower bounds) leads to decidability of some problems. We also put emphasis on open problems. We also discuss formalisms close to parametric timed automata (such as parametric hybrid automata or parametric interrupt timed automata), and we study tools dedicated to PTAs and their extensions.
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ISSN:1433-2779
1433-2787
DOI:10.1007/s10009-017-0467-0