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On transitive closure logic

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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Complementation and Transitive Closure

1999
Over infinite structures, there is a strict hierarchy of languages that is obtained by alternating uses of the least-fixed point operator and negation. For finite structures, we show that the hierarchy collapses to its first-level.
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Transitive dependencies in transaction closures

Proceedings. IDEAS'98. International Database Engineering and Applications Symposium (Cat. No.98EX156), 2002
Complex applications consist of a large set of transactions which are interrelated. There are different kinds of dependencies among transactions of a complex application, e.g. termination or execution dependencies which are constraints on the occurrence of significant transaction events.
K. Schwarz, C. Turker, G. Saake
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Anti-Section Transitive Closure

2021 IEEE 28th International Conference on High Performance Computing, Data, and Analytics (HiPC), 2021
Oded Green   +5 more
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Nested Pebbles and Transitive Closure

2006
First-order logic with k-ary deterministic transitive closure has the same power as two-way k-head deterministic automata that use a finite set of nested pebbles. This result is valid for strings, ranked trees, and in general for families of graphs having a fixed automaton that can be used to traverse the nodes of each of the graphs in the family ...
Joost Engelfriet, Hendrik Jan Hoogeboom
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Modal Logics with Transitive Closure

2014
This last chapter is about the model construction problem in classes of models having relations that are transitive closures of other relations. The main such logics are linear-time temporal logic LTL and propositional dynamic logic PDL. These logics require both blocking and model checking.
Olivier Gasquet   +3 more
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An improved transitive closure algorithm

Computing, 1983
Several 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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Caching transitive closures

Proceedings of the 19th annual conference on Computer Science - CSC '91, 1991
Chandon Chitale, John Sieg
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Multiprocessor Transitive Closure Algorithms

Proceedings [1988] International Symposium on Databases in Parallel and Distributed Systems, 2005
R. Agrawal, H.V. Jagadish
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Shortest Paths and Transitive Closure

1992
Let G = (V, E) be an undirected graph and let l be a function assigning a nonnegative length to each edge. Extend l to domain V x V by defining l(υ, υ) = 0 and l(u, υ) = ∞ if (u, υ) ∉ E. Define the length2 of a path \( p = {e_{1}}{e_{2}}...{e_{n}}{\text{ to be }}l(p) = \Sigma _{{i = 1}}^{n}l({e_{i}}). \).
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