Search results for "Theoretical Computer Science"

Localized forms of the LBB condition and a posteriori estimates for incompressible media problems

2018

Abstract The inf–sup (or LBB) condition plays a crucial role in analysis of viscous flow problems and other problems related to incompressible media. In this paper, we deduce localized forms of this condition that contain a collection of local constants associated with subdomains instead of one global constant for the whole domain. Localized forms of the LBB inequality imply estimates of the distance to the set of divergence free fields. We use them and deduce fully computable bounds of the distance between approximate and exact solutions of boundary value problems arising in the theory of viscous incompressible fluids. The estimates are valid for approximations, which satisfy the incompres…

Mathematical logic and quantum finite state automata

2009

AbstractThis paper is a review of the connection between formulas of logic and quantum finite-state automata in respect to the language recognition and acceptance probability of quantum finite-state automata. As is well known, logic has had a great impact on classical computation, it is promising to study the relation between quantum finite-state automata and mathematical logic. After a brief introduction to the connection between classical computation and logic, the required background of the logic and quantum finite-state automata is provided and the results of the connection between quantum finite-state automata and logic are presented.

From Nerode's congruence to Suffix Automata with mismatches

2009

AbstractIn this paper we focus on the minimal deterministic finite automaton Sk that recognizes the set of suffixes of a word w up to k errors. As first result we give a characterization of the Nerode’s right-invariant congruence that is associated with Sk. This result generalizes the classical characterization described in [A. Blumer, J. Blumer, D. Haussler, A. Ehrenfeucht, M. Chen, J. Seiferas, The smallest automaton recognizing the subwords of a text, Theoretical Computer Science, 40, 1985, 31–55]. As second result we present an algorithm that makes use of Sk to accept in an efficient way the language of all suffixes of w up to k errors in every window of size r of a text, where r is the…

Motif patterns in 2D

2008

AbstractMotif patterns consisting of sequences of intermixed solid and don’t-care characters have been introduced and studied in connection with pattern discovery problems of computational biology and other domains. In order to alleviate the exponential growth of such motifs, notions of maximal saturation and irredundancy have been formulated, whereby more or less compact subsets of the set of all motifs can be extracted, that are capable of expressing all others by suitable combinations. In this paper, we introduce the notion of maximal irredundant motifs in a two-dimensional array and develop initial properties and a combinatorial argument that poses a linear bound on the total number of …

Foreword: Special issue in honor of the 60th Birthday of Professor Alberto Apostolico

2008

On the exhaustive generation of k-convex polyominoes

2017

The degree of convexity of a convex polyomino P is the smallest integer k such that any two cells of P can be joined by a monotone path inside P with at most k changes of direction. In this paper we present a simple algorithm for computing the degree of convexity of a convex polyomino and we show how it can be used to design an algorithm that generates, given an integer k, all k-convex polyominoes of area n in constant amortized time, using space O(n). Furthermore, by applying few changes, we are able to generate all convex polyominoes whose degree of convexity is exactly k.

Approximation Algorithms for Multicoloring Planar Graphs and Powers of Square and Triangular Meshes

2006

A multicoloring of a weighted graph G is an assignment of sets of colors to the vertices of G so that two adjacent vertices receive two disjoint sets of colors. A multicoloring problem on G is to find a multicoloring of G. In particular, we are interested in a minimum multicoloring that uses the least total number of colors. The main focus of this work is to obtain upper bounds on the weighted chromatic number of some classes of graphs in terms of the weighted clique number. We first propose an 11/6-approximation algorithm for multicoloring any weighted planar graph. We then study the multicoloring problem on powers of square and triangular meshes. Among other results, we show that the infi…

Extending formal language hierarchies to higher dimensions

1999

A combinatorial view on string attractors

2021

Abstract The notion of string attractor has recently been introduced in [Prezza, 2017] and studied in [Kempa and Prezza, 2018] to provide a unifying framework for known dictionary-based compressors. A string attractor for a word w = w 1 w 2 ⋯ w n is a subset Γ of the positions { 1 , … , n } , such that all distinct factors of w have an occurrence crossing at least one of the elements of Γ. In this paper we explore the notion of string attractor by focusing on its combinatorial properties. In particular, we show how the size of the smallest string attractor of a word varies when combinatorial operations are applied and we deduce that such a measure is not monotone. Moreover, we introduce a c…

Rapid construction of algebraic axioms from samples

1991

Abstract An axiom is called reliable if it is confirmed in several places in a given sample of algebra. A very effective algorithm for enumerating such axioms is described.