Related papers: Solving Satisfiability of Polynomial Formulas By S…
One of the few available complete methods for checking the satisfiability of sets of polynomial constraints over the reals is the cylindrical algebraic covering (CAlC) method. In this paper, we propose an extension for this method to…
We introduce a new algorithm for checking satisfiability based on a calculus of Dependency sequents (D-sequents). Given a CNF formula F(X), a D-sequent is a record stating that under a partial assignment a set of variables of X is redundant…
In this paper we propose a novel approach for checking satisfiability of non-linear constraints over the reals, called ksmt. The procedure is based on conflict resolution in CDCL style calculus, using a composition of symbolical and…
In this article, we provide a new algorithm for solving constraint satisfaction problems over templates with few subpowers, by reducing the problem to the combination of solvability of a polynomial number of systems of linear equations over…
To advance the field of autonomous robotics, particularly in object search tasks within unexplored environments, we introduce a novel framework centered around the Probable Object Location (POLo) score. Utilizing a 3D object probability…
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…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
This study presents a novel algorithm for identifying the set of extreme points that constitute the exact convex hull of a point set in high-dimensional Euclidean space. The proposed method iteratively solves a sequence of dynamically…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
In their seminal work, Atserias et al. and independently Pipatsrisawat and Darwiche in 2009 showed that CDCL solvers can simulate resolution proofs with polynomial overhead. However, previous work does not address the tightness of the…
The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…
This article is concerned with the application of the program extraction technique to a new class of problems: the synthesis of decision procedures for the classical satisfiability problem that are correct by construction. To this end, we…
Selecting an optimal set of exemplars is critical for good performance of in-context learning. However, prior exemplar search methods narrowly optimize for predictive accuracy, critically neglecting model calibration--a key determinant of…
We previously designed Partial Order Conflict Driven Clause Learning (PO-CDCL), a variation of the satisfiability solving CDCL algorithm with a partial order on decision levels, and showed that it can speed up the solving on problems with a…
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…
We focus on a simulation-based optimization problem of choosing the best design from the feasible space. Although the simulation model can be queried with finite samples, its internal processing rule cannot be utilized in the optimization…
A numerical irreducible decomposition for a polynomial system provides representations for the irreducible factors of all positive dimensional solution sets of the system, separated from its isolated solutions. Homotopy continuation methods…
We study the ideal generated by polynomials vanishing on a semialgebraic set and propose an algorithm to calculate the generators, which is based on some techniques of the cylindrical algebraic decomposition. By applying these, polynomial…