6,252 research outputs found
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
The Complexity of Codiagnosability for Discrete Event and Timed Systems
In this paper we study the fault codiagnosis problem for discrete event
systems given by finite automata (FA) and timed systems given by timed automata
(TA). We provide a uniform characterization of codiagnosability for FA and TA
which extends the necessary and sufficient condition that characterizes
diagnosability. We also settle the complexity of the codiagnosability problems
both for FA and TA and show that codiagnosability is PSPACE-complete in both
cases. For FA this improves on the previously known bound (EXPTIME) and for TA
it is a new result. Finally we address the codiagnosis problem for TA under
bounded resources and show it is 2EXPTIME-complete.Comment: 24 pages
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
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
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
Efficient Emptiness Check for Timed B\"uchi Automata (Extended version)
The B\"uchi non-emptiness problem for timed automata refers to deciding if a
given automaton has an infinite non-Zeno run satisfying the B\"uchi accepting
condition. The standard solution to this problem involves adding an auxiliary
clock to take care of the non-Zenoness. In this paper, it is shown that this
simple transformation may sometimes result in an exponential blowup. A
construction avoiding this blowup is proposed. It is also shown that in many
cases, non-Zenoness can be ascertained without extra construction. An
on-the-fly algorithm for the non-emptiness problem, using non-Zenoness
construction only when required, is proposed. Experiments carried out with a
prototype implementation of the algorithm are reported.Comment: Published in the Special Issue on Computer Aided Verification - CAV
2010; Formal Methods in System Design, 201
Verification of Timed Automata Using Rewrite Rules and Strategies
ELAN is a powerful language and environment for specifying and prototyping
deduction systems in a language based on rewrite rules controlled by
strategies. Timed automata is a class of continuous real-time models of
reactive systems for which efficient model-checking algorithms have been
devised. In this paper, we show that these algorithms can very easily be
prototyped in the ELAN system. This paper argues through this example that
rewriting based systems relying on rules and strategies are a good framework to
prototype, study and test rather efficiently symbolic model-checking
algorithms, i.e. algorithms which involve combination of graph exploration
rules, deduction rules, constraint solving techniques and decision procedures
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