It has been developed a C++ program that generates random fuzzy relations of a given dimension and computes their T-transitive closure (that contains the initial relation) and the new T-transitivized relation (that is contained in the initial relation) for the t-norms minimum, product and Lukasiewicz. It has been computed several distances between both transitive closure and transitivized relat...

In this paper, we present a modified Floyd–Warshall algorithm, where the most time-consumingpart—calculating transitive closure describing self-dependences for each loop statement—is computed applying basis dependence distance vectors derived from all vectors describing self-dependences. We demonstrate that the presented approach reduces the transitive closure calculation time for parameterized...

We establish a general hierarchy theorem for quantiier classes in the innnitary logic L ! 1! on nite structures. In particular, it is shown that no innnitary formula with bounded number of universal quantiiers can express the negation of a transitive closure. This implies the solution of several open problems in nite model theory: On nite structures, positive transitive closure logic is not clo...

We define the notion of a transitive-closure spanner of a directed graph. Given a directed graph G = (V,E) and an integer k ≥ 1, a k-transitive-closure-spanner (k-TC-spanner) of G is a directed graph H = (V,EH) that has (1) the same transitive-closure as G and (2) diameter at most k. These spanners were studied implicitly in access control, property testing, and data structures, and properties ...

We present two new transitive closure algorithms that are based on strong component detection. The algorithms scan the input graph only once without generating partial successor sets for each node. The new algorithms eliminate the redundancy caused by strong components more e ciently than previous transitive closure algorithms. We present statistically sound simulation experiments showing that ...

Note that, in some sense, the O(n2) result is optimal if we approach this problem by storing the transitive closure matrix explicitly (we don’t necessarily have to do this, however, to answer queries). This is because in the worst case, an update can modify Ω(n2) edges in the transitive closure. Next are two results for which the product of the bulk update and query times is O(mn), where m is t...

We have developed some efficient algorithms for computing the transitive closure of a directed graph. This paper presents the algorithms for the problem of reachability. The algorithms, however, can be adapted to deal with path computations and a signitkantJy broader class of queries based on onesided recursions. We analyze these algorithms and compare them to algorithms in the literature. The ...

The problem of knowing and characterizing the transitive behavior of a given cellular automaton is a very interesting topic. This paper provides a matrix representation of the global dynamics in reversible one-dimensional cellular automata with a Welch index 1, i.e. those where the ancestors differ just at one end. We prove that the transitive closure of this matrix shows diverse types of trans...