186 research outputs found
Efficient Algorithms for Morphisms over Omega-Regular Languages
Morphisms to finite semigroups can be used for recognizing omega-regular
languages. The so-called strongly recognizing morphisms can be seen as a
deterministic computation model which provides minimal objects (known as the
syntactic morphism) and a trivial complementation procedure. We give a
quadratic-time algorithm for computing the syntactic morphism from any given
strongly recognizing morphism, thereby showing that minimization is easy as
well. In addition, we give algorithms for efficiently solving various decision
problems for weakly recognizing morphisms. Weakly recognizing morphism are
often smaller than their strongly recognizing counterparts. Finally, we
describe the language operations needed for converting formulas in monadic
second-order logic (MSO) into strongly recognizing morphisms, and we give some
experimental results.Comment: Full version of a paper accepted to FSTTCS 201
Separating Regular Languages with First-Order Logic
Given two languages, a separator is a third language that contains the first
one and is disjoint from the second one. We investigate the following decision
problem: given two regular input languages of finite words, decide whether
there exists a first-order definable separator. We prove that in order to
answer this question, sufficient information can be extracted from semigroups
recognizing the input languages, using a fixpoint computation. This yields an
EXPTIME algorithm for checking first-order separability. Moreover, the
correctness proof of this algorithm yields a stronger result, namely a
description of a possible separator. Finally, we generalize this technique to
answer the same question for regular languages of infinite words
A minimal nonfinitely based semigroup whose variety is polynomially recognizable
We exhibit a 6-element semigroup that has no finite identity basis but
nevertheless generates a variety whose finite membership problem admits a
polynomial algorithm.Comment: 16 pages, 3 figure
Pointlike sets with respect to R and J
We present an algorithm to compute the pointlike subsets of a finite semigroup with respect to the pseudovariety
R of all finite R-trivial semigroups. The algorithm is inspired by Henckell’s algorithm for computing the pointlike
subsets with respect to the pseudovariety of all finite aperiodic semigroups. We also give an algorithm to compute
J-pointlike sets, where J denotes the pseudovariety of all finite J-trivial semigroups. We finally show that, in contrast
with the situation for R, the natural adaptation of Henckell’s algorithm to J computes pointlike sets, but not all
of them.Pessoa French-Portuguese project Egide-
Grices 11113YMFundação para a Ciência e a Tecnologia (FCT
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