形式语言与自动机理论

We prove that the finite condensation rank (FC-rank) of the lexicographic ordering of a context-free language is strictly less than $\omega^\omega$.

A recent study on structural properties of regular and context-free languages has greatly promoted our basic understandings of the complex behaviors of those languages. We continue the study to examine how regular languages behave when they…

This paper introduces an abstract notion of fragments of monadic second-order logic. This concept is based on purely syntactic closure properties. We show that over finite words, every logical fragment defines a lattice of languages with…

It is known that if a B\"uchi context-free language (BCFL) consists of scattered words, then there is an integer $n$, depending only on the language, such that the Hausdorff rank of each word in the language is bounded by $n$. Every BCFL is…

We introduce an automata model for data words, that is words that carry at each position a symbol from a finite alphabet and a value from an unbounded data domain. The model is (semantically) a restriction of data automata, introduced by…

We study regular expressions that use variables, or parameters, which are interpreted as alphabet letters. We consider two classes of languages denoted by such expressions: under the possibility semantics, a word belongs to the language if…

Models of a generalized nondeterminism are defined by limitations on nonde- terministic behavior of a computing device. A regular realizability problem is a problem of verifying existence of a special sort word in a regular language. These…

In this paper we describe an approach to finding the shortest reset word of a finite synchronizing automaton by using a SAT solver. We use this approach to perform an experimental study of the length of the shortest reset word of a finite…

We investigate the problem asking whether the intersection of a context-free language (CFL) and a Petri net language (PNL) is empty. Our contribution to solve this long-standing problem which relates, for instance, to the reachability…

We consider context-free languages equipped with the lexicographic ordering. We show that when the lexicographic ordering of a context-free language is scattered, then its Hausdorff rank is less than $\omega^\omega$. As a corollary of this…

The dot-depth hierarchy is a classification of star-free languages. It is related to the quantifier alternation hierarchy of first-order logic over finite words. We consider fragments of languages with dot-depth 1/2 and dot-depth 1 obtained…

We consider ideals and Boolean combinations of ideals. For the regular languages within these classes we give expressively complete automaton models. In addition, we consider general properties of regular ideals and their Boolean…

We show that it is decidable in exponential time whether the lexicographic ordering of a context-free language is scattered, or a well-ordering.

Over finite words, languages of dot-depth one are expressively complete for alternation-free first-order logic. This fragment is also known as the Boolean closure of existential first-order logic. Here, the atomic formulas comprise order,…

We describe a uniform construction for converting $\omega$-automata with arbitrary acceptance conditions (based on the notion of infinity sets i.e. the set of states visited infinitely often in a run of the automaton) to equivalent…

We consider fragments of first-order logic and as models we allow finite and infinite words simultaneously. The only binary relations apart from equality are order comparison < and the successor predicate +1. We give characterizations of…

This is Chapter 24 in the "AutoMathA" handbook. Finite automata have been used effectively in recent years to define infinite groups. The two main lines of research have as their most representative objects the class of automatic groups…

The (bounded) hairpin completion and its iterated versions are operations on formal lan- guages which have been inspired by the hairpin formation in DNA-biochemistry. The paper answers two questions asked in the literature about the…

We consider the four fragments FO2, the intersection of Sigma2 and FO2, the intersection of Pi2 and FO2, and Delta2 of first-order logic FO[<] over finite and infinite words. For all four fragments, we give characterizations in terms of…

For several semirings S, two weighted finite automata with multiplicities in S are equivalent if and only if they can be connected by a chain of simulations. Such a semiring S is called "proper". It is known that the Boolean semiring, the…