Undecidable problem

About: Undecidable problem is a research topic. Over the lifetime, 3135 publications have been published within this topic receiving 71238 citations.

Alternating Timed Automata over Bounded Time

Abstract: Alternating timed automata are a powerful extension of classical Alur-Dill timed automata that are closed under all Boolean operations. They have played a key role, among others, in providing verification algorithms for prominent specification formalisms such as Metric Temporal Logic. Unfortunately, when interpreted over an infinite dense time domain (such as the reals), alternating time dautomata have an undecidable language emptiness problem. The main result of this paper is that, over bounded time domains, language emptiness for alternating timed automata is decidable (but nonelementary). The proof involves showing decidability of a class of parametric McNaughton games that are played over timed words and that have winning conditions expressed in the monadic logic of order augmented with the distance-one relation. As a corollary, we establish the decidability of the time-bounded model-checking problem for Alur-Dill timed automata against specifications expressed as alternating timed automata.

Controller synthesis for MTL specifications

Abstract: We consider the control problem for timed automata against specifications given as MTL formulas. The logic MTL is a linear-time timed temporal logic which extends LTL with timing constraints on modalities, and recently, its model-checking has been proved decidable in several cases. We investigate these decidable fragments of MTL (full MTL when interpreted over finite timed words, and Safety-MTL when interpreted over infinite timed words), and prove two kinds of results. (1) We first prove that, contrary to model-checking, the control problem is undecidable. Roughly, the computation of a lossy channel system could be encoded as a model-checking problem, and we prove here that a perfect channel system can be encoded as a control problem. (2) We then prove that if we fix the resources of the controller (by resources we mean clocks and constants that the controller can use), the control problem becomes decidable. This decidability result relies on properties of well (and better) quasi-orderings.

The Complexity of Model-Preference Default Theories

Abstract: Most formal theories of default inference have very poor computational properties, and are easily shown to be intractable, or worse, undecidable. We are therefore investigating limited but efficiently computable theories of default reasoning. This paper defines systems of Propositional Model Preference Defaults, which provide a true model-theoretic account of default inference with exceptions. Some of our results extend to other nonmonotonic formalisms, such as Default Logic.

The stability of saturated linear dynamical systems is undecidable

Abstract: We prove that several global properties (global convergence, global asymptotic stability, mortality, and nilpotence) of particular classes of discrete time dynamical systems are undecidable. Such results had been known only for point-to-point properties. We prove these properties undecidable for saturated linear dynamical systems, and for continuous piecewise affine dynamical systems in dimension three. We also describe some consequences of our results on the possible dynamics of such systems.

Containment of Data Graph Queries

Abstract: The graph database model is currently one of the most popular paradigms for storing data, used in applications such as social networks, biological databases and the Semantic Web. Despite the popularity of this model, the development of graph database management systems is still in its infancy, and there are several fundamental issues regarding graph databases that are not fully understood. Indeed, while graph query languages that concentrate on topological properties are now well developed, not much is known about languages that can query both the topology of graphs and their underlying data. Our goal is to conduct a detailed study of static analysis problems for such languages. In this paper we consider the containment problem for several recently proposed classes of queries that manipulate both topology and data: regular queries with memory, regular queries with data tests, and graph XPath. Our results show that the problem is in general undecidable for all of these classes. However, by allowing only positive data comparisons we nd natural fragments that enjoy much better static analysis properties: the containment problem is decidable, and its computational complexity ranges from PSPACE-complete to EXPSPACEcomplete. We also propose extensions of regular queries with an inverse operator, and study query evaluation and query containment for them.