Related papers: Representations for the largest Extension of a clo…

We consider an extension of the unary negation fragment of first-order logic in which arbitrarily many binary symbols may be required to be interpreted as equivalence relations. We show that this extension has the finite model property.…

Though a convergence space is connected if and only if its topological modification is connected, connected subsets differ for the convergence and for its topological modification. We explore for what subsets connectedness for the…

A closure endomorphism of a Hilbert algebra A is a mapping that is simultaneously an endomorphism of and a closure operator on A. It is known that the set CE of all closure endomorphisms of A is a distributive lattice where the meet of two…

The tangled closure of a collection of subsets of a topological space is the largest subset in which each member of the collection is dense. This operation models a logical `tangle modality' connective, of significance in finite model…

This paper describes serial and parallel compositional models of multiple objects with part sharing. Objects are built by part-subpart compositions and expressed in terms of a hierarchical dictionary of object parts. These parts are…

This paper first gives a necessary and sufficient condition that a lattice $L$ can be represented as the collection of all up-sets of a poset. Applying the condition, it obtains a necessary and sufficient condition that a lattice can be…

In this paper we address the problem of generating all elements obtained by the saturation of an initial set by some operations. More precisely, we prove that we can generate the closure by polymorphisms of a boolean relation with a…

Valuation based systems verifying an idempotent property are studied. A partial order is defined between the valuations giving them a lattice structure. Then, two different strategies are introduced to represent valuations: as infimum of…

We investigate the descriptional complexity of operations on semilinear sets. Roughly speaking, a semilinear set is the finite union of linear sets, which are built by constant and period vectors. The interesting parameters of a semilinear…

We show that the decision problem for the basic system of interpretability logic IL is PSPACE-complete. For this purpose we present an algorithm which uses polynomial space with respect to the complexity of a given formula. The existence of…

The serial concatenation of a repetition code with two or more accumulators has the advantage of a simple encoder structure. Furthermore, the resulting ensemble is asymptotically good and exhibits minimum distance growing linearly with…

It is well known that every closure system can be represented by an implicational base, or by the set of its meet-irreducible elements. In Horn logic, these are respectively known as the Horn expressions and the characteristic models. In…

We consider systems of word equations and their solution sets. We discuss some fascinating properties of those, namely the size of a maximal independent set of word equations, and proper chains of solution sets of those. We recall the basic…

It is known that if the underlying iterated function system satisfies the open set condition, then the upper box dimension of an inhomogeneous self-similar set is the maximum of the upper box dimensions of the homogeneous counterpart and…

We propose investigating a summation analog of the paradigm for parallel integration. We make some first steps towards an indefinite summation method applicable to summands that rationally depend on the summation index and a P-recursive…

An additive 2-basis with range n is restricted if its largest element is n/2. Among the restricted 2-bases of given length k, the ones that have the greatest range are extremal restricted. We describe an algorithm that finds the extremal…

It was recently proved that the dualization in lattices given by implicational bases is impossible in output-polynomial time unless P=NP. In this paper, we~show that this result holds even when the premises in the implicational base are of…

Exploring the power of linear programming for combinatorial optimization problems has been recently receiving renewed attention after a series of breakthrough impossibility results. From an algorithmic perspective, the related questions…

The Sequential Multiple Knapsack Problem is a special case of Multiple knapsack problem in which the items sizes are divisible. A characterization of the optimal solutions of the problem and a description of the convex hull of all the…

Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…