7 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
Dense Integer-Complete Synthesis for Bounded Parametric Timed Automata
Ensuring the correctness of critical real-time systems, involving concurrent
behaviors and timing requirements, is crucial. Timed automata extend
finite-state automata with clocks, compared in guards and invariants with
integer constants. Parametric timed automata (PTAs) extend timed automata with
timing parameters. Parameter synthesis aims at computing dense sets of
valuations for the timing parameters, guaranteeing a good behavior. However, in
most cases, the emptiness problem for reachability (i.e., whether the emptiness
of the parameter valuations set for which some location is reachable) is
undecidable for PTAs and, as a consequence, synthesis procedures do not
terminate in general, even for bounded parameters. In this paper, we introduce
a parametric extrapolation, that allows us to derive an underapproximation in
the form of linear constraints containing not only all the integer points
ensuring reachability, but also all the (non-necessarily integer) convex
combinations of these integer points, for general PTAs with a bounded parameter
domain. We also propose two further algorithms synthesizing parameter
valuations guaranteeing unavoidability, and preservation of the untimed
behavior w.r.t. a reference parameter valuation, respectively. Our algorithms
terminate and can output constraints arbitrarily close to the complete result.
We demonstrate their applicability and efficiency using the tool Rom\'eo on two
classical benchmarks.Comment: This is an extended version of the paper by the same authors
published in the proceedings of the 9th International Workshop on
Reachability Problems (RP 2015
Reachability and liveness in parametric timed automata
We study timed systems in which some timing features are unknown parameters.
Parametric timed automata (PTAs) are a classical formalism for such systems but
for which most interesting problems are undecidable. Notably, the parametric
reachability emptiness problem, i.e., whether at least one parameter valuation
allows to reach some given discrete state, is undecidable.
Lower-bound/upper-bound parametric timed automata (L/U-PTAs) achieve
decidability for reachability properties by enforcing a separation of
parameters used as upper bounds in the automaton constraints, and those used as
lower bounds.
In this paper, we first study reachability. We exhibit a subclass of PTAs
(namely integer-points PTAs) with bounded rational-valued parameters for which
the parametric reachability emptiness problem is decidable. Using this class,
we present further results improving the boundary between decidability and
undecidability for PTAs and their subclasses such as L/U-PTAs.
We then study liveness. We prove that:
(1) the existence of at least one parameter valuation for which there exists
an infinite run in an L/U-PTA is PSPACE-complete;
(2) the existence of a parameter valuation such that the system has a
deadlock is however undecidable;
(3) the problem of the existence of a valuation for which a run remains in a
given set of locations exhibits a very thin border between decidability and
undecidability.Comment: This manuscript is an extended version of two conference papers
published in the proceedings of ICFEM 2016 and ACSD 201
Reachability and liveness in parametric timed automata
We study timed systems in which some timing features are unknown parameters.
Parametric timed automata (PTAs) are a classical formalism for such systems but
for which most interesting problems are undecidable. Notably, the parametric
reachability emptiness problem, i.e., the emptiness of the parameter valuations
set allowing to reach some given discrete state, is undecidable.
Lower-bound/upper-bound parametric timed automata (L/U-PTAs) achieve
decidability for reachability properties by enforcing a separation of
parameters used as upper bounds in the automaton constraints, and those used as
lower bounds.
In this paper, we first study reachability. We exhibit a subclass of PTAs
(namely integer-points PTAs) with bounded rational-valued parameters for which
the parametric reachability emptiness problem is decidable. Using this class,
we present further results improving the boundary between decidability and
undecidability for PTAs and their subclasses such as L/U-PTAs.
We then study liveness. We prove that:
(1) deciding the existence of at least one parameter valuation for which
there exists an infinite run in an L/U-PTA is PSpace-complete;
(2) the existence of a parameter valuation such that the system has a
deadlock is however undecidable;
(3) the problem of the existence of a valuation for which a run remains in a
given set of locations exhibits a very thin border between decidability and
undecidability
Parametric updates in parametric timed automata
We introduce a new class of Parametric Timed Automata (PTAs) where we allow
clocks to be compared to parameters in guards, as in classic PTAs, but also to
be updated to parameters. We focus here on the EF-emptiness problem: "is the
set of parameter valuations for which some given location is reachable in the
instantiated timed automaton empty?". This problem is well-known to be
undecidable for PTAs, and so it is for our extension. Nonetheless, if we update
all clocks each time we compare a clock with a parameter and each time we
update a clock to a parameter, we obtain a syntactic subclass for which we can
decide the EF-emptiness problem and even perform the exact synthesis of the set
of rational valuations such that a given location is reachable. To the best of
our knowledge, this is the first non-trivial subclass of PTAs, actually even
extended with parametric updates, for which this is possible
Tools and Algorithms for the Construction and Analysis of Systems
This book is Open Access under a CC BY licence. The LNCS 11427 and 11428 proceedings set constitutes the proceedings of the 25th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019. The total of 42 full and 8 short tool demo papers presented in these volumes was carefully reviewed and selected from 164 submissions. The papers are organized in topical sections as follows: Part I: SAT and SMT, SAT solving and theorem proving; verification and analysis; model checking; tool demo; and machine learning. Part II: concurrent and distributed systems; monitoring and runtime verification; hybrid and stochastic systems; synthesis; symbolic verification; and safety and fault-tolerant systems