This paper discusses an approach to representing and reasoning about constraints over strings. We discuss how many string domains can often be concisely represented using regular languages, and how constraints over strings, and domain operations on sets of strings, can be carried out using this representation.

In this paper, we investigate the state complexities of ( k ∪

The state complexity of basic operations on regular languages has been studied in 9{11]. Here we focus on nite languages. We show that the catenation of two nite languages accepted by an m-state and an n-state DFA, respectively, with m > n is accepted by a DFA of (m ? n + 3)2 n?2 ? 1 states in the two-letter alphabet case, and this bound is shown to be reachable. We also show that the tight upp...

Article history: Received 5 June 2008 Available online 19 March 2009

The following pcf results are proved: 1. Assume that κ > א0 is a weakly compact cardinal. Let μ > 2κ be a singular cardinal of cofinality κ. Then for every regular λ < pp+Γ(κ)(μ) there is an increasing sequence ⟨λi | i < κ⟩ of regular cardinals converging to μ such that λ = tcf( ∏ i<κ λi, <Jbd κ ). 2. Let μ be a strong limit cardinal and θ a cardinal above μ. Suppose that at least one of them h...

Incompleteness and vagueness are inherent properties of knowledge in several real world domains and are particularly pervading in those domains where entities could be better described in natural language. In order to deal with incomplete and vague structured knowledge, several fuzzy extensions of Description Logics (DLs) have been proposed in the literature. In this paper, we address the issue...

In the paper, we continue our study on the state complexity of combined operations on regular languages. We study the state complexities of k ∪ i=1 Li , k ∩ i=1 Li , k ∪ i=1 Li , and k ∩ i=1 Li , for regular languages Li, 1 ≤ i ≤ k. We obtain the exact bounds for these combined operations and show that the state complexities of k ∪ i=1 Li and k ∩ i=1 Li are the same as the mathematical composit...

Ehrenfeucht's Conjecture is equivalent with the ascending chain condition for word equations. A related conjecture concerns the descending chain condition for word equations. We show that if this conjecture holds then an arbitrary in nite language L possesses a nite subset F such that the language L F is a disjoint union of its nite test sets. We prove this consequence of the descending chain c...

We investigate characterizations of the Galois connection sInv–Aut between sets of finitary relations on a base set A and their automorphisms. In particular, for A = ω1, we construct a countable set R of relations that is closed under all invariant operations on relations and under arbitrary intersections, but is not closed under sInvAut. Our structure (A, R) has an ω-categorical first order th...