778 research outputs found
Omega-Regular Model Checking
peer reviewed"Regular model checking" is the name of a family of techniques for analyzing infinite-state systems in which states are represented by words or trees, sets of states by finite automata on these objects, and transitions by finite automata operating on pairs of state encodings, i.e. finite-state transducers. In this context, the central problem is then to compute the iterative closure of a finite-state transducer. This paper addresses the use of regular model-checking like techniques for systems whose states are represented by infinite (omega) words. Its main motivation is to show the feasibility and usefulness of this approach through a combination of the necessary theoretical developments, implementation, and experimentation. The iteration technique that is used is adapted from recent work of the authors on the iteration of finite-word transducers. It proceeds by comparing successive elements of a sequence of approximations of the iteration, detecting an "increment" that is added to move from one approximation to the next, and extrapolating the sequence by allowing arbitrary repetitions of this increment. By restricting oneself to weak deterministic Buchi automata, and using a number of implementation optimizations, examples of significant size can be handled. The proposed transducer iteration technique can just as well be exploited to compute the closure of a given set of states by the transducer iteration, which has proven to be a very effective way of using the technique. Examples such as a leaking gas burner in which time is modeled by real variables have been handled completely within the automata-theoretic setting
Decision Problems for Deterministic Pushdown Automata on Infinite Words
The article surveys some decidability results for DPDAs on infinite words
(omega-DPDA). We summarize some recent results on the decidability of the
regularity and the equivalence problem for the class of weak omega-DPDAs.
Furthermore, we present some new results on the parity index problem for
omega-DPDAs. For the specification of a parity condition, the states of the
omega-DPDA are assigned priorities (natural numbers), and a run is accepting if
the highest priority that appears infinitely often during a run is even. The
basic simplification question asks whether one can determine the minimal number
of priorities that are needed to accept the language of a given omega-DPDA. We
provide some decidability results on variations of this question for some
classes of omega-DPDAs.Comment: In Proceedings AFL 2014, arXiv:1405.527
Enhancing Approximations for Regular Reachability Analysis
This paper introduces two mechanisms for computing over-approximations of
sets of reachable states, with the aim of ensuring termination of state-space
exploration. The first mechanism consists in over-approximating the automata
representing reachable sets by merging some of their states with respect to
simple syntactic criteria, or a combination of such criteria. The second
approximation mechanism consists in manipulating an auxiliary automaton when
applying a transducer representing the transition relation to an automaton
encoding the initial states. In addition, for the second mechanism we propose a
new approach to refine the approximations depending on a property of interest.
The proposals are evaluated on examples of mutual exclusion protocols
On (Omega-)regular model checking
peer reviewedChecking infinite-state systems is frequently done by encoding infinite sets of states as regular languages. Computing such a regular representation of, say, the set of reachable states of a system requires acceleration techniques that can finitely compute the effect of an unbounded number of transitions. Among the acceleration techniques that have been proposed, one finds both specific and generic techniques. Specific techniques exploit the particular type of system being analyzed, for example, a system manipulating queues or integers, whereas generic techniques only assume that the transition relation is represented by a finite-state transducer, which has to be iterated. In this article, we investigate the possibility of using generic techniques in cases where only specific techniques have been exploited so far. Finding that existing generic techniques are often not applicable in cases easily handled by specific techniques, we have developed a new approach to iterating transducers. This new approach builds on earlier work, but exploits a number of new conceptual and algorithmic ideas, often induced with the help of experiments, that give it a broad scope, as well as good performances
26. Theorietag Automaten und Formale Sprachen 23. Jahrestagung Logik in der Informatik: Tagungsband
Der Theorietag ist die Jahrestagung der Fachgruppe Automaten und Formale Sprachen der Gesellschaft für Informatik und fand erstmals 1991 in Magdeburg statt. Seit dem Jahr 1996 wird der Theorietag von einem eintägigen Workshop mit eingeladenen Vorträgen begleitet. Die Jahrestagung der Fachgruppe Logik in der Informatik der Gesellschaft für Informatik fand erstmals 1993 in Leipzig statt. Im Laufe beider Jahrestagungen finden auch die jährliche Fachgruppensitzungen statt. In diesem Jahr wird der Theorietag der Fachgruppe Automaten und Formale Sprachen erstmalig zusammen mit der Jahrestagung der Fachgruppe Logik in der Informatik abgehalten. Organisiert wurde die gemeinsame Veranstaltung von der Arbeitsgruppe Zuverlässige Systeme des Instituts für Informatik an der Christian-Albrechts-Universität Kiel vom 4. bis 7. Oktober im Tagungshotel Tannenfelde bei Neumünster. Während des Tre↵ens wird ein Workshop für alle Interessierten statt finden. In Tannenfelde werden • Christoph Löding (Aachen) • Tomás Masopust (Dresden) • Henning Schnoor (Kiel) • Nicole Schweikardt (Berlin) • Georg Zetzsche (Paris) eingeladene Vorträge zu ihrer aktuellen Arbeit halten. Darüber hinaus werden 26 Vorträge von Teilnehmern und Teilnehmerinnen gehalten, 17 auf dem Theorietag Automaten und formale Sprachen und neun auf der Jahrestagung Logik in der Informatik. Der vorliegende Band enthält Kurzfassungen aller Beiträge. Wir danken der Gesellschaft für Informatik, der Christian-Albrechts-Universität zu Kiel und dem Tagungshotel Tannenfelde für die Unterstützung dieses Theorietags. Ein besonderer Dank geht an das Organisationsteam: Maike Bradler, Philipp Sieweck, Joel Day. Kiel, Oktober 2016 Florin Manea, Dirk Nowotka und Thomas Wilk
Learning to Prove Safety over Parameterised Concurrent Systems (Full Version)
We revisit the classic problem of proving safety over parameterised
concurrent systems, i.e., an infinite family of finite-state concurrent systems
that are represented by some finite (symbolic) means. An example of such an
infinite family is a dining philosopher protocol with any number n of processes
(n being the parameter that defines the infinite family). Regular model
checking is a well-known generic framework for modelling parameterised
concurrent systems, where an infinite set of configurations (resp. transitions)
is represented by a regular set (resp. regular transducer). Although verifying
safety properties in the regular model checking framework is undecidable in
general, many sophisticated semi-algorithms have been developed in the past
fifteen years that can successfully prove safety in many practical instances.
In this paper, we propose a simple solution to synthesise regular inductive
invariants that makes use of Angluin's classic L* algorithm (and its variants).
We provide a termination guarantee when the set of configurations reachable
from a given set of initial configurations is regular. We have tested L*
algorithm on standard (as well as new) examples in regular model checking
including the dining philosopher protocol, the dining cryptographer protocol,
and several mutual exclusion protocols (e.g. Bakery, Burns, Szymanski, and
German). Our experiments show that, despite the simplicity of our solution, it
can perform at least as well as existing semi-algorithms.Comment: Full version of FMCAD'17 pape
Mean-payoff Automaton Expressions
Quantitative languages are an extension of boolean languages that assign to
each word a real number. Mean-payoff automata are finite automata with
numerical weights on transitions that assign to each infinite path the long-run
average of the transition weights. When the mode of branching of the automaton
is deterministic, nondeterministic, or alternating, the corresponding class of
quantitative languages is not robust as it is not closed under the pointwise
operations of max, min, sum, and numerical complement. Nondeterministic and
alternating mean-payoff automata are not decidable either, as the quantitative
generalization of the problems of universality and language inclusion is
undecidable.
We introduce a new class of quantitative languages, defined by mean-payoff
automaton expressions, which is robust and decidable: it is closed under the
four pointwise operations, and we show that all decision problems are decidable
for this class. Mean-payoff automaton expressions subsume deterministic
mean-payoff automata, and we show that they have expressive power incomparable
to nondeterministic and alternating mean-payoff automata. We also present for
the first time an algorithm to compute distance between two quantitative
languages, and in our case the quantitative languages are given as mean-payoff
automaton expressions
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