Undecidable problem

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

Computing universal models under guarded TGDs

Abstract: A universal model of a database D and a set Σ of integrity constraints is a database that extends D, satisfies Σ, and is most general in the sense that it contains sound and complete information. Universal models have a number of applications including answering conjunctive queries, and deciding containment of conjunctive queries, with respect to databases with integrity constraints. Furthermore, they are used in slightly modified form as solutions in data exchange. In general, it is undecidable whether a database possesses a universal model, but in the past few years researchers identified various settings where this problem is decidable, and even efficiently solvable.This paper focuses on computing universal models under finite sets of guarded TGDs, non-conflicting keys, and negative constraints. Such constraints generalize inclusion dependencies, and were recently shown to be expressive enough to capture certain members of the DL-Lite family of description logics. The main result is an algorithm that, given a database without null values and a finite set Σ of such constraints, decides whether there is a universal model, and if so, outputs such a model. If Σ is fixed, the algorithm runs in polynomial time. The algorithm can be extended to cope with databases containing nulls; however, in this case, polynomial running time can be guaranteed only for databases with bounded block size.

Synthesis with Identifiers

Abstract: We consider the synthesis of reactive systems from specifications with identifiers. Identifiers are useful to parametrize the input and output of a reactive system, for example, to state which client requests a grant from an arbiter, or the type of object that a robot is expected to fetch. Traditional reactive synthesis algorithms only handle a constant bounded range of such identifiers. However, in practice, we might not want to restrict the number of clients of an arbiter or the set of object types handled by a robot a priori. We first present a concise automata-based formalism for specifications with identifiers. The synthesis problem for such specifications is undecidable. We therefore give an algorithm that is always sound, and complete for unrealizable safety specifications. Our algorithm is based on computing a pattern-based abstraction of a synthesis game that captures the realizability problem for the specification. The abstraction does not restrict the possible solutions to finite-state ones and captures the obligations for the system in the synthesis game. We present an experimental evaluation based on a prototype implementation that shows the practical applicability of our algorithm.

Computational classification of cellular automata

Abstract: We discuss attempts at the classification of cellular automata, in particular with a view towards decidability. We will see that a large variety of properties relating to the short-term evolution of configurations are decidable in principle, but questions relating to the long-term evolution are typically undecidable. Even in the decidable case, computational hardness poses a major obstacle for the automatic analysis of cellular automata.

AVACS -- Automatic Verification and Analysis of Complex Systems.

Abstract: The recently presented constraint solver HySAT tackles the in general undecidable problem of solving mixed Boolean and non-linear arithmetic constraint formulae over the reals involving transcendental functions. The algorithmic core of HySAT is the iSAT algorithm, a tight integration of the Davis-Putnam-Logemann-Loveland algorithm with interval constraint propagation enriched by enhancements like conflict-driven clause learning and non-chronological backtracking. However, it was an open question whether HySAT’s conflict analysis scheme, an adapted first unique implication point technique as applied in most modern SAT solvers, performs favorably compared to other schemes. In this paper, we compare several conflict analysis heuristics to answer this question. Furthermore, we consider the integration of restarts into the iSAT algorithm and investigate their impact. For our empirical results we use benchmarks from the hybrid systems domain.