10 research outputs found
Revisiting Synthesis for One-Counter Automata
We study the (parameter) synthesis problem for one-counter automata with
parameters. One-counter automata are obtained by extending classical
finite-state automata with a counter whose value can range over non-negative
integers and be tested for zero. The updates and tests applicable to the
counter can further be made parametric by introducing a set of integer-valued
variables called parameters. The synthesis problem for such automata asks
whether there exists a valuation of the parameters such that all infinite runs
of the automaton satisfy some omega-regular property. Lechner showed that (the
complement of) the problem can be encoded in a restricted one-alternation
fragment of Presburger arithmetic with divisibility. In this work (i) we argue
that said fragment, called AERPADPLUS, is unfortunately undecidable.
Nevertheless, by a careful re-encoding of the problem into a decidable
restriction of AERPADPLUS, (ii) we prove that the synthesis problem is
decidable in general and in N2EXP for several fixed omega-regular properties.
Finally, (iii) we give a polynomial-space algorithm for the special case of the
problem where parameters can only be used in tests, and not updates, of the
counter
О разрешимости проблем ограниченности для счетчиковых машин Минского
In the paper the decidability of boundedness problems for counter Minsky machines is investigated. It is proved, that for Minsky machines with two counters the boundedness is partial decidable, but for the total boundedness problem does not even exist a semidecision algorithm. On the other hand, for one-counter Minsky machines all these problems are polinomial (quantitatively of local machine states) decidable.Исследуется разрешимость проблем ограниченности для счетчиковых машин Минского. Доказывается, что для машин Минского с двумя счетчиками проблема ограниченности лишь частично разрешима, а проблема тотальной ограниченности не является даже частично разрешимой. Для односчет-чиковых машин Минского указанные проблемы разрешимы за время, полиномиально зависящее от общего количества локальных состояний счетчиковой машины
Continuous One-Counter Automata
We study the reachability problem for continuous one-counter automata, COCA
for short. In such automata, transitions are guarded by upper and lower bound
tests against the counter value. Additionally, the counter updates associated
with taking transitions can be (non-deterministically) scaled down by a nonzero
factor between zero and one. Our three main results are as follows: (1) We
prove that the reachability problem for COCA with global upper and lower bound
tests is in NC2; (2) that, in general, the problem is decidable in polynomial
time; and (3) that it is decidable in the polynomial hierarchy for COCA with
parametric counter updates and bound tests
Stackless Processing of Streamed Trees
International audienceProcessing tree-structured data in the streaming model is a challenge: capturing regular properties of streamed trees by means of a stack is costly in memory, but falling back to finite-state automata drastically limits the computational power. We propose an intermediate stackless model based on register automata equipped with a single counter, used to maintain the current depth in the tree. We explore the power of this model to validate and query streamed trees. Our main result is an effective characterization of regular path queries (RPQs) that can be evaluated stacklessly-with and without registers. In particular, we confirm the conjectured characterization of tree languages defined by DTDs that are recognizable without registers, by Segoufin and Vianu (2002), in the special case of tree languages defined by means of an RPQ
Vérification efficace de systèmes à compteurs à l'aide de relaxations
Abstract : Counter systems are popular models used to reason about systems in various fields such as the analysis of concurrent or distributed programs and the discovery and verification of business processes. We study well-established problems on various classes of counter systems. This thesis focusses on three particular systems, namely Petri nets, which are a type of model for discrete systems with concurrent and sequential events, workflow nets, which form a subclass of Petri nets that is suited for modelling and reasoning about business processes, and continuous one-counter automata, a novel model that combines continuous semantics with one-counter automata. For Petri nets, we focus on reachability and coverability properties. We utilize directed search algorithms, using relaxations of Petri nets as heuristics, to obtain novel semi-decision algorithms for reachability and coverability, and positively evaluate a prototype implementation. For workflow nets, we focus on the problem of soundness, a well-established correctness notion for such nets. We precisely characterize the previously widely-open complexity of three variants of soundness. Based on our insights, we develop techniques to verify soundness in practice, based on reachability relaxation of Petri nets. Lastly, we introduce the novel model of continuous one-counter automata. This model is a natural variant of one-counter automata, which allows reasoning in a hybrid manner combining continuous and discrete elements. We characterize the exact complexity of the reachability problem in several variants of the model.Les systèmes à compteurs sont des modèles utilisés afin de raisonner sur les systèmes
de divers domaines tels l’analyse de programmes concurrents ou distribués, et
la découverte et la vérification de systèmes d’affaires. Nous étudions des problèmes
bien établis de différentes classes de systèmes à compteurs. Cette thèse se penche sur
trois systèmes particuliers : les réseaux de Petri, qui sont un type de modèle pour les systèmes discrets à
événements concurrents et séquentiels ; les « réseaux de processus », qui forment une sous-classe des réseaux de Petri
adaptée à la modélisation et au raisonnement des processus d’affaires ; les automates continus à un compteur, un nouveau modèle qui combine une
sémantique continue à celles des automates à un compteur.
Pour les réseaux de Petri, nous nous concentrons sur les propriétés d’accessibilité
et de couverture. Nous utilisons des algorithmes de parcours de graphes, avec
des relaxations de réseaux de Petri comme heuristiques, afin d’obtenir de nouveaux
algorithmes de semi-décision pour l’accessibilité et la couverture, et nous évaluons
positivement un prototype.
Pour les «réseaux de processus», nous nous concentrons sur le problème de validité,
une notion de correction bien établie pour ces réseaux. Nous caractérisions
précisément la complexité calculatoire jusqu’ici largement ouverte de trois variantes
du problème de validité. En nous basant sur nos résultats, nous développons des techniques
pour vérifier la validité en pratique, à l’aide de relaxations d’accessibilité dans
les réseaux de Petri. Enfin, nous introduisons le nouveau modèle d’automates continus à un compteur. Ce modèle est une variante naturelle des automates à un compteur, qui permet de
raisonner de manière hybride en combinant des éléments continus et discrets. Nous
caractérisons la complexité exacte du problème d’accessibilité dans plusieurs variantes
du modèle
On validation of XML streams using finite state machines
We study validation of streamed XML documents by means of finite state machines. Previous work has shown that validation is in principle possible by finite state automata, but the construction was prohibitively expensive, giving an exponential-size nondeterministic automaton. Instead, we want to find deterministic automata for validating streamed documents: for them, the complexity of validation is constant per tag. We show that for a reading window of size one and nonrecursive DTDs with one-unambiguous content (i.e. conforming to the current XML standard) there is an algorithm producing a deterministic automaton that validates documents with respect to that DTD. The size of the automaton is at most exponential and we give matching lower bounds. To capture the possible advantages offered by reading windows of size k, we introduce k-unambiguity as a generalization of one-unambiguity, and study the validation against DTDs with k-unambiguous content. We also consider recursive DTDs and give conditions under which they can be validated against by using one-counter automata