The symmetric inverse semigroup I(X) on a set X is the collection of all partial bijections between subsets with composition as algebraic operation. We study minimal Hausdorff topology I(X). present some characterizations it. When countable such Polish.

We present two masked priming lexical decision experiments in which we examined whether a nonword prime word would activate associative/semantic information from its corresponding addition neighbor (e.g., lght-dark via the addition neighbor light), producing associative/semantic priming. The rationale was the following: If a nonword prime with a missing letter produced a semantic/associative pr...

we define minimal cn-dominating graph $mathbf {mcn}(g)$, commonality minimal cn-dominating graph $mathbf {cmcn}(g)$ and vertex minimal cn-dominating graph $mathbf {m_{v}cn}(g)$, characterizations are given for graph $g$ for which the newly defined graphs are connected. further serval new results are developed relating to these graphs.

This paper surveys some recent results on the generation of implicitly given hypergraphs and their applications in Boolean and integer programming, data mining, reliability theory, and combinatorics. Given a monotone property π over the subsets of a finite set V , we consider the problem of incrementally generating the family Fπ of all minimal subsets satisfying property π, when π is given by a...

We consider the problems of enumerating all minimal strongly connected subgraphs and all minimal dicuts of a given directed graph G = (V, E). We show that the first of these problems can be solved in incremental polynomial time, while the second problem is NP-hard: given a collection of minimal dicuts for G, it is NP-complete to tell whether it can be extended. The latter result implies, in par...

The importance and impact of the Boolean satisfiability (SAT) problem in many practical settings is well-known. Besides SAT, a number of computational problems related with Boolean formulas find a wide range of practical applications. Concrete examples for CNF formulas include computing prime implicates (PIs), minimal models (MMs), minimal unsatisfiable subsets (MUSes), minimal equivalent subse...

in this paper, our purpose is twofold. firstly, the tensor andresiduum operations on $l-$nested systems are introduced under thecondition of complete residuated lattice. then we show that$l-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. thus the new representation theorem of$l-$subsets on complete re...

A collectionC of distinct 3-element subsets of the set S = {1, 2, . . . , n} is called an identifying system of the quadruples of S, if every 4-element subset of S contains at least one of the triples in C, and moreover, no two 4-element subsets of S contain exactly the same triples of C. We consider the minimal possible cardinality of such a system, and show, in particular, that for n = 6, 7 a...