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331
The FirstOrder Theory of Ground Tree Rewrite Graphs
"... We prove that the complexity of the uniform firstorder theory of ground tree rewrite graphs is in ATIME(22poly(n) , O(n)). Providing a matching lower bound, we show that there is a fixed ground tree rewrite graph whose firstorder theory is hard for ATIME(22poly(n) , poly(n)) with respect to logspa ..."
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We prove that the complexity of the uniform firstorder theory of ground tree rewrite graphs is in ATIME(22poly(n) , O(n)). Providing a matching lower bound, we show that there is a fixed ground tree rewrite graph whose firstorder theory is hard for ATIME(22poly(n) , poly(n)) with respect
THE COMPLEXITY OF THE FIRSTORDER THEORY OF GROUND TREE REWRITE GRAPHS
, 2014
"... The uniform firstorder theory of ground tree rewrite graphs is the set of all pairs consisting of a ground tree rewrite system and a firstorder sentence that holds in the graph defined by the ground tree rewrite system. We prove that the complexity of the uniform firstorder theory of ground tre ..."
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The uniform firstorder theory of ground tree rewrite graphs is the set of all pairs consisting of a ground tree rewrite system and a firstorder sentence that holds in the graph defined by the ground tree rewrite system. We prove that the complexity of the uniform firstorder theory of ground
Theories for Mutagenicity: A Study in FirstOrder and FeatureBased Induction
 Artificial Intelligence
, 1996
"... A classic problem from chemistry is used to test a conjecture that in domains for which data are most naturally represented by graphs, theories constructed with Inductive Logic Programming (ILP) will significantly outperform those using simpler featurebased methods. One area that has long been asso ..."
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Cited by 159 (30 self)
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A classic problem from chemistry is used to test a conjecture that in domains for which data are most naturally represented by graphs, theories constructed with Inductive Logic Programming (ILP) will significantly outperform those using simpler featurebased methods. One area that has long been
Deciding FirstOrder Properties of Locally TreeDecomposable Graphs
 In Proc. 26th ICALP
, 1999
"... . We introduce the concept of a class of graphs being locally treedecomposable. There are numerous examples of locally treedecomposable classes, among them the class of planar graphs and all classes of bounded valence or of bounded treewidth. We show that for each locally treedecomposable cl ..."
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Cited by 98 (14 self)
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decomposable class C of graphs and for each property ' of graphs that is denable in rstorder logic, there is a linear time algorithm deciding whether a given graph G 2 C has property '. 1 Introduction It is an important task in the theory of algorithms to nd feasible instances of otherwise
INFINITE GRAPHS GENERATED BY TREE REWRITING
, 2002
"... Finite graphs and algorithms on finite graphs are an important tool for the verification of finitestate systems. To transfer the methods for finite systems, at least partially, to infinite systems a theory of infinite graphs with finite representations is needed. In this thesis the class of the tra ..."
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Cited by 16 (2 self)
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of the transition graphs of ground tree rewriting systems is studied. To investigate the structure of ground tree rewriting graphs they are analyzed under the aspect of treewidth of graphs and are compared to already wellstudied classes of graphs, as the class of pushdown graphs and the class of automatic graphs
Extension of FirstOrder Theories into Trees
"... Abstract. We present in this paper an automatic way to combine any firstorder theory T with the theory of finite or infinite trees. First of all, we present a new class of theories that we call zeroinfinitedecomposable and show that every decomposable theory T accepts a decision procedure in the ..."
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Abstract. We present in this paper an automatic way to combine any firstorder theory T with the theory of finite or infinite trees. First of all, we present a new class of theories that we call zeroinfinitedecomposable and show that every decomposable theory T accepts a decision procedure
REWRITING SYSTEMS OVER UNRANKED TREES
, 2006
"... Finite graphs constitute an important tool in various fields of computer science. In order to transfer the theory of finite graphs at least partially to infinite systems, a finite representation of infinite systems is needed. Rewriting systems form a practical model for the finite representation of ..."
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Cited by 1 (0 self)
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of infinite graphs. Among attractive subclasses of rewriting systems is the class of ground tree rewriting systems over ranked trees, which is known to have good algorithmic properties. We investigate these algorithmic properties for two kinds of rewriting systems over unranked trees. For the first introduced
Representing firstorder logic using graphs
 International Conference on Graph Transformations (ICGT), volume 3256 of Lecture Notes in Computer Science
, 2004
"... Abstract. We show how edgelabelled graphs can be used to represent firstorder logic formulae. This gives rise to recursively nested structures, in which each level of nesting corresponds to the negation of a set of existentials. The model is a direct generalisation of the negative application cond ..."
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Cited by 30 (9 self)
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conditions used in graph rewriting, which count a single level of nesting and are thereby shown to correspond to the fragment ∃¬ ∃ of firstorder logic. Vice versa, this generalisation may be used to strengthen the notion of application conditions. We then proceed to show how these nested models may
Ground Tree Rewriting Graphs of Bounded Tree Width
"... We analyze structural properties of ground tree rewriting graphs, generated by rewriting systems that perform replacements at the front of nite, ranked trees. The main result is that the class of ground tree rewriting graphs of bounded tree width exactly corresponds to the class of pushdown gra ..."
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Cited by 4 (1 self)
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We analyze structural properties of ground tree rewriting graphs, generated by rewriting systems that perform replacements at the front of nite, ranked trees. The main result is that the class of ground tree rewriting graphs of bounded tree width exactly corresponds to the class of pushdown
FirstOrder Logic with Reachability Predicates on Infinite Systems
"... This paper focuses on firstorder logic (FO) extended by reachability predicates such that the expressiveness and hence decidability properties lie between FO and monadic secondorder logic (MSO): in FO(R) one can demand that a node is reachably from another by some sequence of edges, whereas in FO( ..."
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introduce a transformation for infinite graphs called setbased unfolding which is based on an idea of Lohrey and Ondrusch. It allows to transfer the decidability of MSO to FO(Reg) onto the class of transformed structures. Finally we extend regular ground tree rewriting with a skeleton tree. We show
Results 1  10
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331