4 research outputs found
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
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
Parametric updates in parametric timed automata
International audienceWe 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
Parametric updates in parametric timed automata
Part 1: Full PapersInternational audienceWe 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