This paper deals with q{series arising from the study of the transitiveclosure problem in random acyclic digraphs. In particularit presents an identity involvingdivisor generatingfunctions which allows to determine the asymptotic behavior of polynomials deened by a general class of recursive equations, including the polynomials for the mean and the variance of the size of the transitive closure...

A brief introduction to the theory of Abstract Interpretation, examplified by constructing a hierarchy of partial traces, reflexive transitive closure, reachable states and intervals abstract semantics of transition systems.

We introduce and study a new percolation model, inspired by recent works on jigsaw percolation, graph bootstrap in polluted environments. Start with an oriented G0 of initially occupied edges n vertices, iteratively occupy additional (oriented) transitivity, the constraint that only open certain random set can ever be occupied. All other are closed, creating obstacles for spread edges. When is ...

In this paper, we introduce a novel approach which is capable of computing transitive closure optimally for relations with varying properties. The new approach is derived from two classical software fault tolerance methods, namely N-Version Programming and Recovery Blocks. We show how these methods are used to optimise the computation of transitive closure for database relations. The performanc...

This paper investigates a Description Logic, namely SHI+, which extends SHI by adding transitive closure of roles. The resulting logic SHI+ allows transitive closure of roles to occur not only in concept inclusion axioms but also in role inclusion axioms. We show that SHI+ is decidable by devising a terminating, sound and complete algorithm for deciding satisfiability of concepts in SHI+ with r...

We present new implementations of BSP/CGM algorithms for the Transitive Closure Problem. Our strategies deal with size of the message and communication rounds, problems that cause inefficiency in the implementations of the transitive closure algorithms. The algorithms were implemented using LAM/MPI in two Beowulfs. The implementation results show the efficiency and scalability of the presented ...

We present a framework for the estimation of the size of binary recursively defined relations. We show how the framework can be used to provide estimating algo rithms for the size of the transitive closure and generalizations of the transitive closure, and also show that for bounded degree relations, the algorithm runs in linear time. Such estimating algorithms are essential if database systems...

Finding strongly connected components (SCCs) in the state-space of discrete-state models is a critical task in formal verification of LTL and fair CTL properties, but the potentially huge number of reachable states and SCCs constitutes a formidable challenge. This paper is concerned with computing the sets of states in SCCs or terminal SCCs of asynchronous systems. Because of its advantages in ...