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The satisfiability problem of hybrid logics with the downarrow binder is known to be undecidable. This initiated a research program on decidable and tractable fragments. In this paper, we investigate the effect of restricting the…
We prove the uniqueness of the infinite length axisymmetric solution to the capillary equation. We observe that capillary equation can be viewed, at large depth, as a perturbation of an integrable two-dimensional differential system.…
An ansatz describing in terms of formal asymptotic decompositions a leading term of asymptotics of the $n$ three-dimensional like-charged quantum particles scattering problem solution is suggested. The description of the solution in those…
The quantified constraint satisfaction problem (QCSP) is a powerful framework for modelling computational problems. The general intractability of the QCSP has motivated the pursuit of restricted cases that avoid its maximal complexity. In…
A notion of alternating timed automata is proposed. It is shown that such automata with only one clock have decidable emptiness problem over finite words. This gives a new class of timed languages which is closed under boolean operations…
We show the NP-completeness of the existential theory of term algebras with the Knuth-Bendix order by giving a nondeterministic polynomial-time algorithm for solving Knuth-Bendix ordering constraints.
We provide simple necessary and sufficient conditions under which a path constitutes a solution to an infinite-horizon, continuous-time optimal control problem. We prove transversality conditions under standard assumptions. We also present…
In this paper we prove that the uniform one-dimensional guarded fragment, which is a natural polyadic generalization of the guarded two-variable logic, has the Craig interpolation property. We will also prove that the satisfiability problem…
A compact real analytic Riemannian manifold M admits a canonical complexification with plurisubharmonic exhaustion function satisfying the homogeneous complex Monge-Ampere equation, called a Grauert tube. From the point of view of complex…
We present sufficient conditions for the existence of positive solutions for a class of fractional singular boundary value problems in presence of Caputo fractional derivative. Further, the nonlinearity involved has singularity with respect…
This paper proves the NP-completeness of the reachability problem for the class of flat counter machines with difference bounds and, more generally, octagonal relations, labeling the transitions on the loops. The proof is based on the fact…
Exponentiable functors between quantaloid-enriched categories are characterized in elementary terms. The proof goes as follows: the elementary conditions on a given functor translate into existence statements for certain adjoints that obey…
This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original finite space, and constitutes an upper bound for the…
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…
In this paper, we focus on qualitative temporal sequences of topological information. We firstly consider the context of topological temporal sequences of length greater than 3 describing the evolution of regions at consecutive time points.…
Interpreting three-leaf binary trees or {\em rooted triples} as constraints yields an entailment relation, whereby binary trees satisfying some rooted triples must also thus satisfy others, and thence a closure operator, which is known to…
I shall describe a general model-theoretic task to construct expansions of pseudofinite structures and discuss several examples of particular relevance to computational complexity. Then I will present one specific situation where finding a…
We study the Constraint Satisfaction Problem CSP(A), where A is first-order definable in (Z;+,1) and contains +. We prove such problems are either in P or NP-complete.
We introduce the $k$-variable-occurrence fragment, which is the set of terms having at most $k$ occurrences of variables. We give a sufficient condition for the decidability of the equational theory of the $k$-variable-occurrence fragment…
In this paper we show that the problem of checking consistency of a knowledge base in the Description Logic ALCM is ExpTime-complete. The M stands for meta-modelling as defined by Motz, Rohrer and Severi. To show our main result, we define…