String languages recognizable in (deterministic) log-space are characterized either by two-way (deterministic) multi-head automata, or following Immerman, by first-order logic with (deterministic) transitive closure. Here we elaborate this result, and match the number of heads to the arity of the transitive closure. More precisely, first-order logic with k-ary deterministic transitive closure h...

In this thesis we investigate fully dynamic algorithms for path problems on directed graphs. In particular, we focus on two of the most fundamental path problems: fully dynamic transitive closure and fully dynamic single-source shortest paths. The rst part of the thesis presents a new technique which makes it possible to reduce fully dynamic transitive closure to the problem of reevaluating pol...

The Abiteboul and Beeri algebra for complex objects can express a query whose meaning is transitive closure, but the algorithm naturally associated to this query needs exponential space. We show that any other query in the algebra which expresses transitive closure needs exponential space. This proves that in general the powerset is an intractable operator for implementing xpoint queries.

We consider entailment problems involving powerful constraint languages such as guarded existential rules, in which additional semantic restrictions are put on a set of distinguished relations. We consider restricting a relation to be transitive, restricting a relation to be the transitive closure of another relation, and restricting a relation to be a linear order. We give some natural general...

In this paper we prove that any distance-balanced graph G with ∆(G) ≥ |V (G)| − 3 is regular. Also we define notion of distancebalanced closure of a graph and we find distance-balanced closures of trees T with ∆(T ) ≥ |V (T )| − 3.

Although, the notion of trust has been considered as a primitive for establishing relationships among nodes in ad-hoc networks, syntax and metrics of trust are not well defined. This paper studies computing of trust in ad-hoc networks and makes the following three contributions. Firstly, the notion of trust is formalized in terms of predict functions and strategy functions. Namely, the notion o...

The soft set theory is a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. Babitha and Sunil [Soft set relations and function, Computers and Mathematics with Applications 60 (2010) 1840–1849] introduced the notion of soft set relations as a soft subset of the Cartesian product of soft sets and discussed m...

We present a fault-independent redundancy identification algorithm. The controllabilities and observabilities are defined as Boolean variables and represented on an implication graph. A major enhancement over previously published results is that we include all direct and partial implications, as well as node fixation. The transitive closure, whose computation now requires a new algorithm, provi...

There are fast known algorithms to compute the transitive closure of a fuzzy relation, but there are only a few different algorithms that compute T-transitive low approximations of a fuzzy relation. A fast method to compute a T-transitive low approximation of a reflexive and symmetric fuzzy relation is given for any continuous tnorm, spending O(n) time.

We propose a class hierarchy for loops in a loop nest. Its purpose is to help identify the proper code generation methods for a space-time mapped nest. We illustrate the hierarchy and its use on a loop nest for computing the reeexive transitive closure of a graph.