A linear inference is a valid inequality of Boolean algebra in which each variable occurs at most once on side. In this work we leverage recently developed graphical representations formulae to build an implementation that capable more efficiently searching for switch-medial-independent inferences. We use it find four `minimal' 8-variable independent inferences and also prove no smaller ones ex...

Abstract. In this paper, we address the problem for enumerating the number of finite field elements with prescribed trace and co-trace in case of arbitrary characteristic p. We show that this problem can be reduced to solving a system of p − 1 linear equations with matrix of coefficients a slight modification of circulant matrix formed by the Kloosterman sums over the field Fp. The presented ap...

We are given a set S of n points in the Euclidean plane. assume that is general position. A simple polygon P an empty if each vertex point and every either outside or P. In this paper, we consider problem enumerating all polygons set. To design efficient enumeration algorithm, use reverse search by Avis Fukuda with child lists. propose algorithm enumerates O(n2 |ϵ(S) |)-time, where ϵ(S) S. More...

The homomorphism problem for relational structures is an abstract way of formulating constraint satisfaction problems (CSP) and various problems in database theory. The decision version of the homomorphism problem received a lot of attention in literature; in particular, the way the graph-theoretical structure of the variables and constraints influences the complexity of the problem is intensiv...

This report is a comprehensive review of the field of molecular enumeration from early isomer counting theories to evolutionary algorithms that design molecules in silico. The core of the review is a detail account on how molecules are counted, enumerated, and sampled. The practical applications of molecular enumeration are also reviewed for chemical information, structure elucidation, molecula...