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The expressivity of XPath with transitive closure
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems, 2006We extend Core XPath, the navigational fragment of XPath 1.0, with transitive closure and path equalities. The resulting language, Regular XPATH≈, is expressively complete for FO* (first-order logic extended with a transitive closure operator that can be applied to formulas with exactly two free variables). As a corollary, we obtain that Regular XPATH≈
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Parallel transitive closure and transitive reduction algorithms
Proceedings. PARBASE-90: International Conference on Databases, Parallel Architectures, and Their Applications, 2002The authors provide distinct algorithms for computing transitive closure and transitive reduction with sequential time complexities of O( Sigma e/sub i/) and O(n/sup 2/+ Sigma e/sub i/), respectively, and parallel time complexities of O(e/sub i/) And O(n+e/sub i/), respectively.
Pintsang Chang, Lawrence J. Henschen
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The transitive closure of a random digraph
Random Structures & Algorithms, 1990AbstractIn a random n‐vertex digraph, each arc is present with probability p, independently of the presence or absence of other arcs. We investigate the structure of the strong components of a random digraph and present an algorithm for the construction of the transitive closure of a random digraph.
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2005
We present Ehrenfeucht-Fraisse games for transitive closure logic (FO + TC) and for quantifier classes in (FO + TC). With this method we investigate the fine structure of positive transitive closure logic (FO + pos TC), and identify an infinite quantifier hierarchy inside (FO + pos TC), formed by interleaving universal quantifiers and TC-operators.
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We present Ehrenfeucht-Fraisse games for transitive closure logic (FO + TC) and for quantifier classes in (FO + TC). With this method we investigate the fine structure of positive transitive closure logic (FO + pos TC), and identify an infinite quantifier hierarchy inside (FO + pos TC), formed by interleaving universal quantifiers and TC-operators.
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On computing the transitive closure of a state transition relation
Proceedings of the 30th international on Design automation conference - DAC '93, 1993We describe a new, recursive-descent procedure for the computation of the transitive closure of a transition relation. This procedure is the classic binary matrix procedure of [1], adapted to a BDD data structure. We demonstrate its efficacy when compared to standard iterative methods.
Yusuke Matsunaga +2 more
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Cache-friendly implementations of transitive closure
Proceedings 2001 International Conference on Parallel Architectures and Compilation Techniques, 2002The topic of cache performance has been well studied in recent years. Compiler optimizations exist and optimizations have been done for many problems. Much of this work has focused on dense linear algebra problems. At first glance, the Floyd--Warshall algorithm appears to fall into this category.
Michael Penner, Viktor K. Prasanna
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An improved transitive closure algorithm
Computing, 1983Several efficient transitive closure algorithms operate on the strongly connected components of a digraph, some of them using Tarjan's algorithm [17]. Exploiting facts from graph theory and the special properties of Tarjan's algorithm we develop a new, improved algorithm.
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The Serial Transitive Closure Problem for Trees
SIAM Journal on Computing, 1995Summary: The serial transitive closure problem is the problem, given a directed graph \(G\) and a list of edges, called closure edges, which are in the transitive closure of the graph, to generate all the closure edges from edges in \(G\). A nearly linear upper bound is given on the number of steps in optimal solutions to the serial transitive closure ...
Maria Luisa Bonet, Samuel R. Buss
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Fast Dynamic Transitive Closure with Lookahead
Algorithmica, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Piotr Sankowski, Marcin Mucha
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The dimension of the negation of transitive closure
Journal of Symbolic Logic, 1995AbstractWe prove that any positive elementary (least fixed point) induction expressing the negation of transitive closure on finite nondirected graphs requires at least two recursion variables.
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