In this paper we investigate the parallel complexity of computing the stable model of acyclic general logic programs Within this class of logic programs we consider the cases of negative and de nite logic programs Both cases are proved to be P complete We prove the same for a related problem namely that of computing the kernel of a directed acyclic graph

We study logics and games over dynamically changing structures. Van Benthem’s sabotage modal logic consists of modal logic with a cross-model modality referring to submodels from which a transition has been removed. We add constructors for forming least and greatest monadic fixed-points to that logic and obtain the sabotage μ-calculus. We introduce backup parity games as an extension of standar...

This paper presents a range of quantitative extensions for the temporal logic CTL. We enhance temporal modalities with the ability to constrain the number of states satisfying certain sub-formulas along paths. By selecting the combinations of Boolean and arithmetic operations allowed in constraints, one obtains several distinct logics generalizing CTL. We provide a thorough analysis of their ex...

In this report we give a formal definition of the sliding block puzzle Rush Hour and we report on the proof showing that Rush Hour is PSPACE-complete from “The nondeterministic constraint logic model of computation: Reductions and applications” by Hearn and Demaine (Proceedings ICALP 2002).

The generalization of the satisfiability problem with arbitrary quantifiers is a challenging problem of both theoretical and practical relevance. Being PSPACE-complete, it provides a canonical model for solving other PSPACE tasks which naturally arise in AI. Effective SAT-based solvers have been designed very recently for the special case of boolean constraints. We propose to consider the more ...

Systems with an arbitrary number of homogeneous processes occur in many applications. The Parameterized Model Checking Problem (PMCP) is to determine whether a temporal property is true of every size instance of the system. We consider systems formed by a synchronous parallel composition of a single control process with an arbitrary number of homogeneous user processes, and show that the PMCP i...

Graded path modalities count the number of paths satisfying a property, and generalize the existential (E) and universal (A) path modalities of CTL∗. The resulting logic is denoted GCTL∗, and is a very powerful logic since (as we show) it is equivalent, over trees, to monadic path logic. We settle the complexity of the satisfiability problem of GCTL∗, i.e., 2ExpTime-Complete, and the complexity...

Model checking probabilistic knowledge of memoryful semantics is undecidable, even for a simple formula concerning the reachability of probabilistic knowledge of a single agent. This result suggests that the usual approach of tackling undecidable model checking problems, by finding syntactic restrictions over the logic language, may not suffice. In this paper, we propose to work with an additio...

In this paper we prove that the general avalanche problem AP is in NC for the Kadanoff sandpile model in one dimension, answering an open problem of [2]. Thus adding one more item to the (slowly) growing list of dimension sensitive problems since in higher dimensions the problem is P-complete (for monotone sandpiles).

The commuting variety is the pairs of n × n matrices (X, Y) such that XY = YX. We introduce the diagonal commutator scheme, { (X, Y) : XY − YX is diagonal } , which we prove to be a reduced complete intersection, one component of which is the commuting variety. (We conjecture there to be only one other component.) The diagonal commutator scheme has a flat degeneration to the scheme { (X, Y) : X...