1,846 research outputs found
Language Emptiness of Continuous-Time Parametric Timed Automata
Parametric timed automata extend the standard timed automata with the
possibility to use parameters in the clock guards. In general, if the
parameters are real-valued, the problem of language emptiness of such automata
is undecidable even for various restricted subclasses. We thus focus on the
case where parameters are assumed to be integer-valued, while the time still
remains continuous. On the one hand, we show that the problem remains
undecidable for parametric timed automata with three clocks and one parameter.
On the other hand, for the case with arbitrary many clocks where only one of
these clocks is compared with (an arbitrary number of) parameters, we show that
the parametric language emptiness is decidable. The undecidability result
tightens the bounds of a previous result which assumed six parameters, while
the decidability result extends the existing approaches that deal with
discrete-time semantics only. To the best of our knowledge, this is the first
positive result in the case of continuous-time and unbounded integer
parameters, except for the rather simple case of single-clock automata
MTL-Model Checking of One-Clock Parametric Timed Automata is Undecidable
Parametric timed automata extend timed automata (Alur and Dill, 1991) in that
they allow the specification of parametric bounds on the clock values. Since
their introduction in 1993 by Alur, Henzinger, and Vardi, it is known that the
emptiness problem for parametric timed automata with one clock is decidable,
whereas it is undecidable if the automaton uses three or more parametric
clocks. The problem is open for parametric timed automata with two parametric
clocks. Metric temporal logic, MTL for short, is a widely used specification
language for real-time systems. MTL-model checking of timed automata is
decidable, no matter how many clocks are used in the timed automaton. In this
paper, we prove that MTL-model checking for parametric timed automata is
undecidable, even if the automaton uses only one clock and one parameter and is
deterministic.Comment: In Proceedings SynCoP 2014, arXiv:1403.784
LTL Parameter Synthesis of Parametric Timed Automata
The parameter synthesis problem for parametric timed automata is undecidable
in general even for very simple reachability properties. In this paper we
introduce restrictions on parameter valuations under which the parameter
synthesis problem is decidable for LTL properties. The investigated bounded
integer parameter synthesis problem could be solved using an explicit
enumeration of all possible parameter valuations. We propose an alternative
symbolic zone-based method for this problem which results in a faster
computation. Our technique extends the ideas of the automata-based approach to
LTL model checking of timed automata. To justify the usefulness of our
approach, we provide experimental evaluation and compare our method with
explicit enumeration technique.Comment: 23 pages, extended versio
Revisiting Reachability in Timed Automata
We revisit a fundamental result in real-time verification, namely that the
binary reachability relation between configurations of a given timed automaton
is definable in linear arithmetic over the integers and reals. In this paper we
give a new and simpler proof of this result, building on the well-known
reachability analysis of timed automata involving difference bound matrices.
Using this new proof, we give an exponential-space procedure for model checking
the reachability fragment of the logic parametric TCTL. Finally we show that
the latter problem is NEXPTIME-hard
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