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68
Finite Presentations of Infinite Structures: Automata and Interpretations
 Theory of Computing Systems
, 2002
"... We study definability problems and algorithmic issues for infinite structures that are finitely presented. After a brief overview over different classes of finitely presentable structures, we focus on structures presented by automata or by modeltheoretic interpretations. ..."
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Cited by 42 (3 self)
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We study definability problems and algorithmic issues for infinite structures that are finitely presented. After a brief overview over different classes of finitely presentable structures, we focus on structures presented by automata or by modeltheoretic interpretations.
Logics for unranked trees: an overview
 Logical Methods in Computer Science 2, Issue 3, Paper 2
, 2006
"... Vol. 2 (3:2) 2006, pp. 1–31 www.lmcsonline.org ..."
Expressive Languages for Path Queries over GraphStructured Data
, 2010
"... For many problems arising in the setting of graph querying (such as finding semantic associations in RDF graphs, exact and approximate pattern matching, sequence alignment, etc.), the power of standard languages such as the widely studied conjunctive regular path queries (CRPQs) is insufficient in a ..."
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Cited by 28 (10 self)
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For many problems arising in the setting of graph querying (such as finding semantic associations in RDF graphs, exact and approximate pattern matching, sequence alignment, etc.), the power of standard languages such as the widely studied conjunctive regular path queries (CRPQs) is insufficient in at least two ways. First, they cannot output paths and second, more crucially, they cannot express relations among paths. We thus propose a class of extended CRPQs, called ECRPQs, which add regular relations on tuples of paths, and allow path variables in the heads of queries. We provide several examples of their usefulness in querying graph structured data, and study their properties. We analyze query evaluation and representation of tuples of paths in the output by means of automata. We present a detailed analysis of data and combined complexity of queries, and consider restrictions that lower the complexity of ECRPQs to that of relational conjunctive queries. We study the containment problem, and look at further extensions with firstorder features, and with nonregular relations that express arithmetic properties of paths, based on the lengths and numbers of occurrences of labels.
Automatic Structures: Richness and Limitations
 PROCEEDINGS OF THE 19TH IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE (IEEE COMPUTER SOCIETY
, 2004
"... This paper addresses the question of whether a given algebraic structure has an automatic presentation and, in the case that it has, how similar its presentations are. That is, what is the complexity of finding out whether two presentations stand for the same algebraic structure. So the first topic ..."
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Cited by 26 (9 self)
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This paper addresses the question of whether a given algebraic structure has an automatic presentation and, in the case that it has, how similar its presentations are. That is, what is the complexity of finding out whether two presentations stand for the same algebraic structure. So the first topic is that of characterising the class of automatic structures. The automatic Boolean algebras are characterised, and it is proven that the free Abelian group of infinite rank and many Frasse limits do not have automatic presentations. In particular, the countably infinite random graph and the universal partial order do not have automatic presentations. Furthermore, no infinite integral domain is automatic. The second topic of the paper is the isomorphism problem. We prove that the complexity of the isomorphism problem for the class of all automatic ... complete.
Finite Model Theory and Descriptive Complexity
, 2002
"... This is a survey on the relationship between logical definability and computational complexity on finite structures. Particular emphasis is given to gamebased evaluation algorithms for various logical formalisms and to logics capturing complexity classes. In addition to the ..."
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Cited by 23 (7 self)
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This is a survey on the relationship between logical definability and computational complexity on finite structures. Particular emphasis is given to gamebased evaluation algorithms for various logical formalisms and to logics capturing complexity classes. In addition to the
Definable Relations and FirstOrder Query Languages over Strings
"... We study analogs of classical relational calculus in the context of strings. We start by studying string logics. Taking a classical modeltheoretic approach, we fix a set of string operations and look at the resulting collection of definable relations. These form an algebra  a class of nary relati ..."
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Cited by 22 (8 self)
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We study analogs of classical relational calculus in the context of strings. We start by studying string logics. Taking a classical modeltheoretic approach, we fix a set of string operations and look at the resulting collection of definable relations. These form an algebra  a class of nary relations for every n, closed under projection and Boolean operations. We show that by choosing the string vocabulary carefully, we get string logics that have desirable properties: computable evaluation and normal forms. We identify five distinct models and study the differences in their modeltheory and complexity of evaluation. We identify a subset of these models which have additional attractive properties, such as finite VC dimension and quantifier elimination. Once you have a logic,
PrefixRecognisable Graphs and Monadic SecondOrder Logic
, 2001
"... We present several characterisations of the class of prefixrecognisable ..."
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Cited by 20 (1 self)
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We present several characterisations of the class of prefixrecognisable
Width parameters beyond treewidth and their applications
 Computer Journal
, 2007
"... Besides the very successful concept of treewidth (see [Bodlaender, H. and Koster, A. (2007) Combinatorial optimisation on graphs of bounded treewidth. These are special issues on Parameterized Complexity]), many concepts and parameters measuring the similarity or dissimilarity of structures compare ..."
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Cited by 19 (0 self)
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Besides the very successful concept of treewidth (see [Bodlaender, H. and Koster, A. (2007) Combinatorial optimisation on graphs of bounded treewidth. These are special issues on Parameterized Complexity]), many concepts and parameters measuring the similarity or dissimilarity of structures compared to trees have been born and studied over the past years. These concepts and parameters have proved to be useful tools in many applications, especially in the design of efficient algorithms. Our presented novel look at the contemporary developments of these ‘width ’ parameters in combinatorial structures delivers—besides traditional treewidth and derived dynamic programming schemes—also a number of other useful parameters like branchwidth, rankwidth (cliquewidth) or hypertreewidth. In this contribution, we demonstrate how ‘width ’ parameters of graphs and generalized structures (such as matroids or hypergraphs), can be used to improve the design of parameterized algorithms and the structural analysis in other applications on an abstract level.
A ModelTheoretic Approach to Regular String Relations
, 2001
"... We study algebras of de nable string relations  classes of regular nary relations that arise as the definable sets within a model whose carrier is the set of all strings. We show that the largest such algebra  the collection of regular relations  has some quite undesirable computational and mode ..."
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Cited by 15 (4 self)
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We study algebras of de nable string relations  classes of regular nary relations that arise as the definable sets within a model whose carrier is the set of all strings. We show that the largest such algebra  the collection of regular relations  has some quite undesirable computational and modeltheoretic properties. In contrast, we exhibit several definable relation algebras that have much tamer behavior: for example, they admit quantifier elimination, and have finite VC dimension. We show that the properties of a definable relation algebra are not at all determined by the onedimensional definable sets. We give models whose definable sets are all starfree, but whose binary relations are quite complex, as well as models whose definable sets include all regular sets, but which are much more restricted and tractable than the full algebra of regular relations.
On the Automata Size for Presburger Arithmetic
 In Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS 2004
, 2004
"... Automata provide an effective mechanization of decision procedures for Presburger arithmetic. However, only crude lower and upper bounds are known on the sizes of the automata produced by this approach. In this paper, we prove that the number of states of the minimal deterministic automaton for a Pr ..."
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Cited by 10 (2 self)
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Automata provide an effective mechanization of decision procedures for Presburger arithmetic. However, only crude lower and upper bounds are known on the sizes of the automata produced by this approach. In this paper, we prove that the number of states of the minimal deterministic automaton for a Presburger arithmetic formula is triple exponentially bounded in the length of the formula. This upper bound is established by comparing the automata for Presburger arithmetic formulas with the formulas produced by a quantifier elimination method. We also show that this triple exponential bound is tight (even for nondeterministic automata). Moreover, we provide optimal automata constructions for linear equations and inequations.