We obtain several new dynamic algorithms for maintaining the transitive closure of a directed graph and several other algorithms for answering reachability queries without explicitly maintaining a transitive closure matrix. Among our algorithms are: (i) A decremental algorithm for maintaining the transitive closure of a directed graph, through an arbitrary sequence of edge deletions, in O(mn) t...

The notion of a transitive closure of a fuzzy relation is very useful for clustering in pattern recognition, for fuzzy databases, etc. It is based on translating the standard definition of transitivity and transitive closure into fuzzy terms. This definition works fine, but to some extent it does not fully capture our understanding of transitivity. The reason is that this definition is based on...

A technique for extracting coarse-grained parallelism available in loops is presented. It is based on splitting a set of dependence relations into two sets. The first one is to be used for generating code scanning slices while the second one permits us to insert send and receive functions to synchronize the slices execution. The paper presents a way demonstrating how to remove redundant synchro...

Though the transitive closure of a reflexive and symmetric fuzzy relation R is unique and there are several algorithms to calculate it, there can be many transitive openings (maximal T -indistinguishability operators among the ones smaller than or equal to R). This paper presents a method to calculate transitive openings of a reflexive and symmetric fuzzy relation R. It is worth noticing that a...

We present a model of transitive inference (TI) using ACT-R which strengthens the hypothesis that TI is not dependent on underlying sequential ordering of stimuli, but rather on the learning of productions. We nevertheless find a weakness in the ACT-R sub-symbolic learning system and suggest improvements.

Abstract We propose a cut-free cyclic system for transitive closure logic (TCL) based on form of hypersequents , suitable automated reasoning via proof search. show that previously proposed sequent systems are incomplete basic validities from Kleene Algebra (KA) and propositional dynamic ( $$\text {PDL}$$ PDL </mml...