Related papers: Satisfiability in multi-valued circuits
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
In a sequence of seminal results in the 80's, Kaltofen showed that the complexity class VP is closed under taking factors. A natural question in this context is to understand if other natural classes of multivariate polynomials, for…
We study the computational complexity of model checking and satisfiability problems of polyadic modal logics extended with permutations and Boolean operators on accessibility relations. First, we show that the combined complexity of the…
A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fixed set B of Boolean functions. We consider the problem of determining whether two given constraint…
We propose a method for exact circuit synthesis using a discrete gate set, as required for fault-tolerant quantum computing. Our approach translates the problem of synthesizing a gate specified by its unitary matrix into a boolean…
Finding a quantum computing method to solve nondeterministic polynomial time (NP)-complete problems is currently of paramount importance in quantum information science. Here an experiment is presented to demonstrate the use of Rydberg atoms…
In this paper, we present a new, graph-based modeling approach and a polynomial-sized linear programming (LP) formulation of the Boolean satisfiability problem (SAT). The approach is illustrated with a numerical example.
This is the second in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. The research in this article aims to find conditions of an algorithmic nature that are necessary and sufficient to…
We give a complexity dichotomy for the problem of computing the partition function of a weighted Boolean constraint satisfaction problem. Such a problem is parameterized by a set of rational-valued functions, which generalize constraints.…
Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in…
In many decision-making processes, one may prefer multiple solutions to a single solution, which allows us to choose an appropriate solution from the set of promising solutions that are found by algorithms. Given this, finding a set of…
The rank of a finite algebraic structure with a single binary operation is the minimum number of elements needed to express every other element under the closure of the operation. In the case of groups, the previous best algorithm for…
We design a deterministic subexponential time algorithm that takes as input a multivariate polynomial $f$ computed by a constant-depth circuit over rational numbers, and outputs a list $L$ of circuits (of unbounded depth and possibly with…
In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time…
We initiate a systematic study of the computational complexity of the Constraint Satisfaction Problem (CSP) over finite structures that may contain both relations and operations. We show the close connection between this problem and a…
Fix a finite group $G$. We study the computational complexity of counting problems of the following flavor: given a group $\Gamma$, count the number of homomorphisms $\Gamma \to G$. Our first result establishes that this problem is…
Generalised Satisfiability Problems (or Boolean Constraint Satisfaction Problems), introduced by Schaefer in 1978, are a general class of problem which allow the systematic study of the complexity of satisfiability problems with different…
The boxicity of a graph $G$ is the minimum dimension $d$ that admits a representation of $G$ as the intersection graph of a family of axis-parallel boxes in $\mathbb{R}^d$. Computing boxicity is an NP-hard problem, and there are few known…
In this paper, we consider bounded width circuits and nondeterministic circuits in three somewhat new directions. In the first part of this paper, we mainly consider bounded width circuits. The main purpose of this part is to prove that…
The computational complexity of solving random 3-Satisfiability (3-SAT) problems is investigated. 3-SAT is a representative example of hard computational tasks; it consists in knowing whether a set of alpha N randomly drawn logical…