353 research outputs found
Reachability in Two-Clock Timed Automata is PSPACE-complete
Recently, Haase, Ouaknine, and Worrell have shown that reachability in two-clock timed automata is log-space equivalent to reachability in bounded one-counter automata. We show that reachability in bounded one-counter automata is PSPACE-complete
Weak Singular Hybrid Automata
The framework of Hybrid automata, introduced by Alur, Courcourbetis,
Henzinger, and Ho, provides a formal modeling and analysis environment to
analyze the interaction between the discrete and the continuous parts of
cyber-physical systems. Hybrid automata can be considered as generalizations of
finite state automata augmented with a finite set of real-valued variables
whose dynamics in each state is governed by a system of ordinary differential
equations. Moreover, the discrete transitions of hybrid automata are guarded by
constraints over the values of these real-valued variables, and enable
discontinuous jumps in the evolution of these variables. Singular hybrid
automata are a subclass of hybrid automata where dynamics is specified by
state-dependent constant vectors. Henzinger, Kopke, Puri, and Varaiya showed
that for even very restricted subclasses of singular hybrid automata, the
fundamental verification questions, like reachability and schedulability, are
undecidable. In this paper we present \emph{weak singular hybrid automata}
(WSHA), a previously unexplored subclass of singular hybrid automata, and show
the decidability (and the exact complexity) of various verification questions
for this class including reachability (NP-Complete) and LTL model-checking
(PSPACE-Complete). We further show that extending WSHA with a single
unrestricted clock or extending WSHA with unrestricted variable updates lead to
undecidability of reachability problem
Model Checking One-clock Priced Timed Automata
We consider the model of priced (a.k.a. weighted) timed automata, an
extension of timed automata with cost information on both locations and
transitions, and we study various model-checking problems for that model based
on extensions of classical temporal logics with cost constraints on modalities.
We prove that, under the assumption that the model has only one clock,
model-checking this class of models against the logic WCTL, CTL with
cost-constrained modalities, is PSPACE-complete (while it has been shown
undecidable as soon as the model has three clocks). We also prove that
model-checking WMTL, LTL with cost-constrained modalities, is decidable only if
there is a single clock in the model and a single stopwatch cost variable
(i.e., whose slopes lie in {0,1}).Comment: 28 page
A Note on Fault Diagnosis Algorithms
In this paper we review algorithms for checking diagnosability of
discrete-event systems and timed automata. We point out that the diagnosability
problems in both cases reduce to the emptiness problem for (timed) B\"uchi
automata. Moreover, it is known that, checking whether a discrete-event system
is diagnosable, can also be reduced to checking bounded diagnosability. We
establish a similar result for timed automata. We also provide a synthesis of
the complexity results for the different fault diagnosis problems.Comment: Note: This paper is an extended version of the paper published in the
proceedings of CDC'09, 48th IEEE Conference on Decision and Control and 28th
Chinese Control Conference, Shanghai, P.R. China, December 2009
Optimal infinite scheduling for multi-priced timed automata
This paper is concerned with the derivation of infinite schedules for timed automata that are in some sense optimal. To cover a wide class of optimality criteria we start out by introducing an extension of the (priced) timed automata model that includes both costs and rewards as separate modelling features. A precise definition is then given of what constitutes optimal infinite behaviours for this class of models. We subsequently show that the derivation of optimal non-terminating schedules for such double-priced timed automata is computable. This is done by a reduction of the problem to the determination of optimal mean-cycles in finite graphs with weighted edges. This reduction is obtained by introducing the so-called corner-point abstraction, a powerful abstraction technique of which we show that it preserves optimal schedules
Optimal Reachability in Divergent Weighted Timed Games
Weighted timed games are played by two players on a timed automaton equipped
with weights: one player wants to minimise the accumulated weight while
reaching a target, while the other has an opposite objective. Used in a
reactive synthesis perspective, this quantitative extension of timed games
allows one to measure the quality of controllers. Weighted timed games are
notoriously difficult and quickly undecidable, even when restricted to
non-negative weights. Decidability results exist for subclasses of one-clock
games, and for a subclass with non-negative weights defined by a semantical
restriction on the weights of cycles. In this work, we introduce the class of
divergent weighted timed games as a generalisation of this semantical
restriction to arbitrary weights. We show how to compute their optimal value,
yielding the first decidable class of weighted timed games with negative
weights and an arbitrary number of clocks. In addition, we prove that
divergence can be decided in polynomial space. Last, we prove that for untimed
games, this restriction yields a class of games for which the value can be
computed in polynomial time
Interrupt Timed Automata: verification and expressiveness
We introduce the class of Interrupt Timed Automata (ITA), a subclass of
hybrid automata well suited to the description of timed multi-task systems with
interruptions in a single processor environment. While the reachability problem
is undecidable for hybrid automata we show that it is decidable for ITA. More
precisely we prove that the untimed language of an ITA is regular, by building
a finite automaton as a generalized class graph. We then establish that the
reachability problem for ITA is in NEXPTIME and in PTIME when the number of
clocks is fixed. To prove the first result, we define a subclass ITA- of ITA,
and show that (1) any ITA can be reduced to a language-equivalent automaton in
ITA- and (2) the reachability problem in this subclass is in NEXPTIME (without
any class graph). In the next step, we investigate the verification of real
time properties over ITA. We prove that model checking SCL, a fragment of a
timed linear time logic, is undecidable. On the other hand, we give model
checking procedures for two fragments of timed branching time logic. We also
compare the expressive power of classical timed automata and ITA and prove that
the corresponding families of accepted languages are incomparable. The result
also holds for languages accepted by controlled real-time automata (CRTA), that
extend timed automata. We finally combine ITA with CRTA, in a model which
encompasses both classes and show that the reachability problem is still
decidable. Additionally we show that the languages of ITA are neither closed
under complementation nor under intersection
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