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The recognizability of sets of graphs is a robust property
"... Once the set of finite graphs is equipped with an algebra structure (arising from the definition of operations that generalize the concatenation of words), one can define the notion of a recognizable set of graphs in terms of finite congruences. Applications to the construction of efficient algorith ..."
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Cited by 14 (9 self)
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Once the set of finite graphs is equipped with an algebra structure (arising from the definition of operations that generalize the concatenation of words), one can define the notion of a recognizable set of graphs in terms of finite congruences. Applications to the construction of efficient algorithms and to the theory of contextfree sets of graphs follow naturally. The class of recognizable sets depends on the signature of graph operations. We consider three signatures related respectively to Hyperedge Replacement (HR) contextfree graph grammars, to Vertex Replacement (VR) contextfree graph grammars, and to modular decompositions of graphs. We compare the corresponding classes of recognizable sets. We show that they are robust in the sense that many variants of each signature (where in particular operations are defined by quantifierfree formulas, a quite flexible framework) yield the same notions of recognizability. We prove that for graphs without large complete bipartite subgraphs, HRrecognizability and VRrecognizability coincide. The same combinatorial condition equates HRcontextfree and VRcontextfree sets of graphs. Inasmuch as possible, results are formulated in the more general framework of relational structures. 1
A survey on small fragments of firstorder logic over finite words
 International Journal of Foundations of Computer Science
, 2008
"... 1 ..."
EFFICIENT ALGORITHMS FOR MEMBERSHIP IN BOOLEAN HIERARCHIES OF REGULAR LANGUAGES
, 2008
"... The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbiddenchain characterizations for the single levels of these hierarchies and obtain ..."
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Cited by 2 (1 self)
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The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbiddenchain characterizations for the single levels of these hierarchies and obtain the following results: • The classes of the Boolean hierarchy over level Σ1 of the dotdepth hierarchy are decidable in NL (previously only the decidability was known). The same remains true if predicates mod d for fixed d are allowed. • If modular predicates for arbitrary d are allowed, then the classes of the Boolean hierarchy over level Σ1 are decidable. • For the restricted case of a twoletter alphabet, the classes of the Boolean hierarchy over level Σ2 of the StraubingThérien hierarchy are decidable in NL. This is the first decidability result for this hierarchy. • The membership problems for all mentioned Booleanhierarchy classes are logspace manyone hard for NL. • The membership problems for quasiaperiodic languages and for dquasiaperiodic languages are logspace manyone complete for PSPACE.
FRAGMENTS OF FIRSTORDER LOGIC OVER INFINITE WORDS (EXTENDED ABSTRACT)
 SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE
, 2008
"... We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of firstorder logic FO[<] for ωlanguages: Σ2, ∆2, FO 2 ∩ Σ2 (and by duality FO 2 ∩ Π2), and FO 2. These descriptions extend the respective results for finite words. In particu ..."
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Cited by 2 (0 self)
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We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of firstorder logic FO[<] for ωlanguages: Σ2, ∆2, FO 2 ∩ Σ2 (and by duality FO 2 ∩ Π2), and FO 2. These descriptions extend the respective results for finite words. In particular, we relate the above fragments to language classes of certain (unambiguous) polynomials. An immediate consequence is the decidability of the membership problem of these classes, but this was shown before by Wilke [20] and Bojańczyk [2] and is therefore not our main focus. The paper is about the interplay of algebraic, topological, and language theoretic properties.
Kleene theorems for product systems
"... Abstract. We prove Kleene theorems for two subclasses of labelled product systems which are inspired from wellstudied subclasses of 1bounded Petri nets. For product Tsystems we define a corresponding class of expressions. The algorithms from systems to expressions and in the reverse direction are ..."
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Abstract. We prove Kleene theorems for two subclasses of labelled product systems which are inspired from wellstudied subclasses of 1bounded Petri nets. For product Tsystems we define a corresponding class of expressions. The algorithms from systems to expressions and in the reverse direction are both polynomial time. For product free choice systems with a restriction of structural cyclicity, that is, the initial global state is a feedback vertex set, going from systems to expressions is still polynomial time; in the reverse direction it is polynomial time with access to an NP oracle for finding deadlocks. 1
www.stacsconf.org EFFICIENT ALGORITHMS FOR MEMBERSHIP IN BOOLEAN HIERARCHIES OF REGULAR LANGUAGES
, 2008
"... Abstract. The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbiddenchain characterizations for the single levels of these hierarchies ..."
Abstract
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Abstract. The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbiddenchain characterizations for the single levels of these hierarchies and obtain the following results: • The classes of the Boolean hierarchy over level Σ1 of the dotdepth hierarchy are decidable in NL (previously only the decidability was known). The same remains true if predicates mod d for fixed d are allowed. • If modular predicates for arbitrary d are allowed, then the classes of the Boolean hierarchy over level Σ1 are decidable. • For the restricted case of a twoletter alphabet, the classes of the Boolean hierarchy over level Σ2 of the StraubingThérien hierarchy are decidable in NL. This is the first decidability result for this hierarchy. • The membership problems for all mentioned Booleanhierarchy classes are logspace manyone hard for NL. • The membership problems for quasiaperiodic languages and for dquasiaperiodic languages are logspace manyone complete for PSPACE.