Related papers: On a Certain NP-Complete Problem
Majority-SAT is the problem of determining whether an input $n$-variable formula in conjunctive normal form (CNF) has at least $2^{n-1}$ satisfying assignments. Majority-SAT and related problems have been studied extensively in various AI…
We introduce the problem of temporal coverability for realizability and synthesis. Namely, given a language of words that must be covered by a produced system, how to automatically produce such a system. We consider the case of coverability…
In the maximum constraint satisfaction problem (MAX CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given finite domain to the variables so…
NP complete problem is one of the most challenging issues. The question of whether all problems in NP are also in P is generally considered one of the most important open questions in mathematics and theoretical computer science as it has…
Whether the satisfiability of any formula F of propositional calculus can be determined in polynomial time is an open question. I propose a simple procedure based on some real world mechanisms to tackle this problem. The main result is the…
This paper develops a parallel computational solver for computing all satifying assignments of a Boolean system of equations defined by Boolean functions of several variables. While there are we known solvers for satisfiability of Boolean…
The exact cover problem is a classical NP-hard problem with broad applications in the area of AI. Algorithm DXZ is a method to count exact covers representing by zero-suppressed binary decision diagrams (ZBDDs). In this paper, we propose a…
Normal surface theory, a tool to represent surfaces in a triangulated 3-manifold combinatorially, is ubiquitous in computational 3-manifold theory. In this paper, we investigate a relaxed notion of normal surfaces where we remove the…
Many natural optimization problems derived from $\sf NP$ admit bilevel and multilevel extensions in which decisions are made sequentially by multiple players with conflicting objectives, as in interdiction, adversarial selection, and…
In many submodular optimization applications, datasets are naturally partitioned into disjoint subsets. These scenarios give rise to submodular optimization problems with partition-based constraints, where the desired solution set should be…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…
Completions play an important r\^ole for studying structure by supplying elements that in some sense ``ought to be." Among these, the Dedekind-MacNeille completion is of particular importance. In 1968 Janowitz provided necessary and…
Boolean Satisfiability (SAT) is arguably the archetypical NP-complete decision problem. Progress in SAT solving algorithms has motivated an ever increasing number of practical applications in recent years. However, many practical uses of…
The requirement of a language to be conditionally decomposable is imposed on a specification language in the coordination supervisory control framework of discrete-event systems. In this paper, we present a polynomial-time algorithm for the…
We show that the problem of deciding whether the vertex set of a graph can be covered with at most two bicliques is in NP$\cap$coNP. We thus almost determine the computational complexity of a problem whose status has remained open for quite…
Using a graph-theoretic approach, we derive a new sufficient condition for observability of a Boolean control network (BCN). Based on this condition, we describe two algorithms: the first selects a set of nodes so that observing this set…
Given a set U of alternatives, a choice (correspondence) on U is a contractive map c defined on a family Omega of nonempty subsets of U. Semantically, a choice c associates to each menu A in Omega a nonempty subset c(A) of A comprising all…
Generating diverse solutions to the Boolean Satisfiability Problem (SAT) is a hard computational problem with practical applications for testing and functional verification of software and hardware designs. We explore the way to generate…
Although the CSP (constraint satisfaction problem) is NP-complete, even in the case when all constraints are binary, certain classes of instances are tractable. We study classes of instances defined by excluding subproblems. This approach…