Related papers: Counting Constraints in Flat Array Fragments
In this paper, we investigate the expressive power and the algorithmic properties of weighted expressions, which define functions from finite words to integers. First, we consider a slight extension of an expression formalism, introduced by…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
Presburger arithmetic is the first-order theory of the natural numbers with addition (but no multiplication). We characterize sets that can be defined by a Presburger formula as exactly the sets whose characteristic functions can be…
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…
We present a new and compelling approach to the efficient solution of important computational problems that arise in the context of abstract argumentation. Our approach makes known algorithms defined for restricted fragments generally…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, including the case of constrained degrees. Our approach relies heavily on analytic combinatorics and on the notion of patchwork to…
We study VC-dimension of short formulas in Presburger Arithmetic, defined to have a bounded number of variables, quantifiers and atoms. We give both lower and upper bounds, which are tight up to a polynomial factor in the bit length of the…
Counting logics with a bounded number of variables form one of the central concepts in descriptive complexity theory. Although they restrict the number of variables that a formula can contain, the variables can be nested within scopes of…
We consider the extension of the two-variable guarded fragment logic with local Presburger quantifiers. These are quantifiers that can express properties such as "the number of incoming blue edges plus twice the number of outgoing red edges…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
Configuring consists in simulating the realization of a complex product from a catalog of component parts, using known relations between types, and picking values for object attributes. This highly combinatorial problem in the field of…
Word equations are a crucial element in the theoretical foundation of constraint solving over strings. A word equation relates two words over string variables and constants. Its solution amounts to a function mapping variables to constant…
Weighted First-Order Model Counting (WFOMC) computes the weighted sum of the models of a first-order theory on a given finite domain. WFOMC has emerged as a fundamental tool for probabilistic inference. Algorithms for WFOMC that run in…
Difference constraints have been used for termination analysis in the literature, where they denote relational inequalities of the form x' <= y + c, and describe that the value of x in the current state is at most the value of y in the…
We derive a formula for expressing free cumulants whose entries are products of random variables in terms of the lattice structure of non-crossing partitions. We show the usefulness of that result by giving direct and conceptually simple…
We investigate finite deterministic automata in sets with non-homogeneous atoms: integers with successor. As there are uncount- ably many deterministic finite automata in this setting, we restrict our attention to automata with semilinear…
Craig interpolation has emerged as an effective means of generating candidate program invariants. We present interpolation procedures for the theories of Presburger arithmetic combined with (i) uninterpreted predicates (QPA+UP), (ii)…
Cardinality constraints or, more generally, weight constraints are well recognized as an important extension of answer-set programming. Clearly, all common algorithmic tasks related to programs with cardinality or weight constraints - like…
We consider the problem of automatically proving resource bounds. That is, we study how to prove that an integer-valued resource variable is bounded by a given program expression. Automatic resource-bound analysis has recently received…