Related papers: Spectral and Modular Analysis of #P Problems
Solving a decision theory problem usually involves finding the actions, among a set of possible ones, which optimize the expected reward, possibly accounting for the uncertainty of the environment. In this paper, we introduce the…
Satisfiability problem (SAT) is a cornerstone of computational complexity with broad industrial applications, and it remains challenging to optimize modern SAT solvers in real-world settings due to their intricate architectures. While…
We introduce the idea of an understanding with respect to a set of clauses as a satisfying truth assignment explained by the contexts of the literals in the clauses. Following this idea, we present a mechanical process that obtains, if it…
Spectral estimation can be preformed using the so called THREE-like approach. Such method leads to a convex optimization problem whose solution is characterized through its dual problem. In this paper, we show that the dual problem can be…
A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…
We lay the foundations of a new theory for algorithms and computational complexity by parameterizing the instances of a computational problem as a moduli scheme. Considering the geometry of the scheme associated to 3-SAT, we separate P and…
The subset sum problem is known to be an NP-hard problem in the field of computer science with the fastest known approach having a run-time complexity of $O(2^{0.3113n})$. A modified version of this problem is known as the perfect sum…
This paper reviews the recent literature on solving the Boolean satisfiability problem (SAT), an archetypal NP-complete problem, with the help of machine learning techniques. Despite the great success of modern SAT solvers to solve large…
We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…
Most recent MaxSAT algorithms rely on a succession of calls to a SAT solver in order to find an optimal solution. In particular, several algorithms take advantage of the ability of SAT solvers to identify unsatisfiable subformulas. Usually,…
In this paper, we first formalize the problem to be solved, i.e., the Scatter Problem (SP). We then show that SP cannot be deterministically solved. Next, we propose a randomized algorithm for this problem. The proposed solution is…
Presentation of set matrices and demonstration of their efficiency as a tool using the path/cycle problem.
Recent research in areas such as SAT solving and Integer Linear Programming has shown that the performances of a single arbitrarily efficient solver can be significantly outperformed by a portfolio of possibly slower on-average solvers. We…
This paper presents a novel SAT-based approach for the computation of extensions in abstract argumentation, with focus on preferred semantics, and an empirical evaluation of its performances. The approach is based on the idea of reducing…
The aim of this short note is mainly pedagogical. It summarizes some knowledge about Boolean satisfiability (SAT) and the P=NP? problem in an elementary mathematical language. A convenient scheme to visualize and manipulate CNF formulae is…
This is a commentary on, and critique of, Latif Salum's paper titled "Tractability of One-in-three $\mathrm{3SAT}$: $\mathrm{P} = \mathrm{NP}$." Salum purports to give a polynomial-time algorithm that solves the $\mathrm{NP}$-complete…
Going as far as possible at SAT problem solving is the main aim of our work. For this sake we have made use of quantum computing from its two, on practice, main models of computation. They have required some reformulations over the former…
We define the concept of a monotonic theory and show how to build efficient SMT (SAT Modulo Theory) solvers, including effective theory propagation and clause learning, for such theories. We present examples showing that monotonic theories…
The classical satisfiability problem (SAT) is used as a natural and general tool to express and solve combinatorial problems that are in NP. We postulate that provability for implicational intuitionistic propositional logic (IIPC) can serve…
The paper considers a split inverse problem involving component equilibrium problems in Hilbert spaces. This problem therefore is called the split equilibrium problem (SEP). It is known that almost solution methods for solving problem (SEP)…