Related papers: On two-variable guarded fragment logic with expres…

The data-complexity of both satisfiability and finite satisfiability for the two-variable fragment with counting is NP-complete; the data-complexity of both query-answering and finite query-answering for the two-variable guarded fragment…

One-dimensional fragment of first-order logic is obtained by restricting quantification to blocks of existential (universal) quantifiers that leave at most one variable free. We investigate this fragment over words and trees, presenting a…

The first-order theory of addition over the natural numbers, known as Presburger arithmetic, is decidable in double exponential time. Adding an uninterpreted unary predicate to the language leads to an undecidable theory. We sharpen the…

We study Two-Variable First-Order Logic, FO2, under semantic constraints that model hierarchically structured data. Our first logic extends FO2 with a linear order < and a chain of increasingly coarser equivalence relations E_1, E_2, ... .…

We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain. Data values can be compared wrt.\ equality. As the satisfiability problem for this logic is undecidable in…

The finite satisfiability problem of two-variable logic extended by a linear order successor and a preorder successor is shown to be undecidable.

In logics with the Craig interpolation property (CIP) the existence of an interpolant for an implication follows from the validity of the implication. In logics with the projective Beth definability property (PBDP), the existence of an…

This paper introduces a variant of the classical edge coloring problem in graphs that can be applied to an offline scheduling problem for crossbar switches. We show that the problem is NP-complete, develop three lower bounds bounds on the…

We consider first-order logic over the subword ordering on finite words, where each word is available as a constant. Our first result is that the $\Sigma_1$ theory is undecidable (already over two letters). We investigate the decidability…

We give a sufficient condition under which every finite-satisfiable formula of a given PCTL fragment has a model with at most doubly exponential number of states (consequently, the finite satisfiability problem for the fragment is in…

We consider three variants of the problem of finding a maximum weight restricted $2$-matching in a subcubic graph $G$. (A $2$-matching is any subset of the edges such that each vertex is incident to at most two of its edges.) Depending on…

We identify a fragment of Presburger arithmetic enriched with free function symbols and cardinality constraints for interpreted sets, which is amenable to automated analysis. We establish decidability and complexity results for such a…

In this paper, we consider the satisfiability problem for string logic with equations, regular membership and Presburger constraints over length functions. The difficulty comes from multiple occurrences of string variables making…

This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…

Treewidth (tw) is an important parameter that, when bounded, yields tractability for many problems. For example, graph problems expressible in Monadic Second Order (MSO) logic and QUANTIFIED SAT or, more generally, QUANTIFIED CSP, are FPT…

We consider expansions of Presburger arithmetic with families of monadic polynomial predicates. (Examples of such predicates are the set of perfect squares, or the set of integers of the form $2n^3-5n+3$, etc.) Although the full attendant…

We investigate the possibility of proving upper bounds on Hadwiger's number of a graph with partial information, mirroring several known upper bounds for the chromatic number. For each such bound we determine whether the corresponding bound…

By Fagin's Theorem, NP contains precisely those problems that can be described by formulas starting with an existential second-order quantifier, followed by only first-order quantifiers (ESO formulas). Subsequent research refined this…

We extend the two-variable logic on data words with guarded regular binary predicates of the form $\widetilde{L}(x,y)$ that is true if positions $x$ and $y$ are in the same class and the factor strictly between $x$ and $y$ is in the regular…

This paper provides an NP procedure that decides whether a linear-exponential system of constraints has an integer solution. Linear-exponential systems extend standard integer linear programs with exponential terms $2^x$ and remainder terms…