Complexity of Testing Reachability in Matroids

Recognizing Matroids

Let $E$ be a finite set and $\mathcal P$, $\mathcal S$, $\mathcal L$ three classes of subsets of $E$, and $r$ a function defined on $2^E$. In this paper, we give an algorithm for testing if the quadruple $(\mathcal P, \mathcal S, \mathcal L, r)$ is the locked structure of a given matroid, i.e., recognizing if $(\mathcal P, \mathcal S, \mathcal L, r)$ defines a matroid. This problem is intractab...

Fault Detection of Reachability Testing with Game Theoretic Approach

--This paper presents a game theoretic approach to fault detection of reachability testing. Physical systems are susceptible to fault at any time. Due to this reason the problem of determining and reacting to fault detection has received a greater attention in today’s era. In this paper we study the fault detection of reachability tesing from a game theoretic point of view. Reachability testing...

CATEGORICAL RELATIONS AMONG MATROIDS, FUZZY MATROIDS AND FUZZIFYING MATROIDS

The aim of this paper is to study the categorical relations betweenmatroids, Goetschel-Voxman’s fuzzy matroids and Shi’s fuzzifying matroids.It is shown that the category of fuzzifying matroids is isomorphic to that ofclosed fuzzy matroids and the latter is concretely coreflective in the categoryof fuzzy matroids. The category of matroids can be embedded in that offuzzifying matroids as a simul...

Analyzing Reachability for Some Petri Nets With Fast Growing Markings

Using linear algebraic techniques, we analyse the computational complexity of testing reachability in Petri nets for which markings can grow very fast. This leads to two subclasses of Petri nets for which the reachability problem is PSPACE-complete. These subclasses are not contained in any other subclass for which complexity of the reachability problem was known, such as those given in Esparza...

Space Complexity of Reachability Testing in Labelled Graphs