Let X be a (finite or infinite) set and let G be a (finite or infinite) group of automorphisms of X. Thus G acts on X and for every g E G the sequence k&x is a permutation of X. For every subset Y of X and every g E G, let g Y be the set of all elements gy, for y E Y. Clearly 1 g Y 1 = 1 Y 1 for every finite Y, and this defines an action of the group G on the power set of X. The orbit of a subs...

Attribute grammars and logic programs are two well investigated formalisms, which were related in DM85] for the restricted class of simple logic programs. In this paper we deene the more restricted class of very simple logic programs and we prove that the problem of deciding, whether a given logic program is (very) simple, is NP{complete.

In this note, a direct proof is given of the NP-completeness of a variant of Graph Coloring, i.e., a generic proof is given, similar to the proof of Cook of the NPcompleteness of Satisfiability. Then, transformations from this variant of Graph Coloring to Independent Set and to Satisfiability are given. These proofs could be useful in an educational setting, where basics of the theory of NP-com...

We present a new proof of NP-completeness for the problem of solving instances of the Japanese pencil puzzle Kakuro (also known as Cross-Sum). While the NP-completeness of Kakuro puzzles has been shown before [T. Seta. The complexity of CROSS SUM. IPSJ SIG Notes, AL-84:51–58, 2002], there are still two interesting aspects to our proof: we show NP-completeness for a new variant of Kakuro that ha...

Given an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a non-crossing matching between point-object pairs. We show that when the objects we match the points to are finite point sets, the problem is NP-complete in general, and polynomial when the objects are on a line or when their number is at most 2. When the objects are line segments,...

Let G be an undirected graph on n nodes, and let k be an integer that divides n. A k-equipartition π of G is a partition of V (G) into k equal-sized pieces V1, . . ., Vk. A pair Vi, Vj of distinct sets in π is called a bad pair if there is at least one edge vi −− vj of E(G) such that vi ∈ Vi and vj ∈ Vj . The parameterized equipartition problem is: given G and k, find an optimal k-equipartition...

We prove the NP-completeness of a problem, we call Social Group Commonality (SGC), which queries the commonality amongst the objects ‘touched’ by a collections of agents while executing an action. Although it naturally arises in several contexts, e.g., to profile the behaviour of a collection of system users, SGC has, to the authors’ knowledge, been ignored. Our proof of SGC NP-completeness con...

We prove the NP-completeness of the so-called Social Group Commonality (SGC) problem which queries the commonality among the objects ‘touched’ by collections of agents while executing an action. Although it naturally arises in several contexts, e.g., in profiling the behavior of a collection of system users, SGC (to the authors’ knowledge) has been ignored. Our proof of SGC NP-completeness cons...

We introduce a new set of problems based on the Chain Editing problem. In our version of Chain Editing, we are given a set of anonymous participants and a set of undisclosed tasks that every participant attempts. For each participant-task pair, we know whether the participant has succeeded at the task or not. We assume that participants vary in their ability to solve tasks, and that tasks vary ...