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Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets. Originally introduced by Collins in the 1970s for use in quantifier elimination it has since found numerous applications within…
This article introduces SatHyS (SAT HYbrid Solver), a novel hybrid approach for propositional satisfiability. It combines local search and conflict driven clause learning (CDCL) scheme. Each time the local search part reaches a local…
Multidimensional systems are becoming increasingly important as they provide a promising tool for estimation, simulation and control, while going beyond the traditional setting of one-dimensional systems. The analysis of multidimensional…
Boolean satisfiability problem has applications in various fields. An efficient algorithm to solve satisfiability problem can be used to solve many other problems efficiently. The input of satisfiability problem is a finite set of clauses.…
This paper presents a novel algorithm for constructing a sum-of-squares (SOS) decomposition for positive semi-definite polynomials with rational coefficients. Unlike previous methods that typically yield SOS decompositions with…
We prove that there exists a deterministic configuration of Conflict Driven Clause Learning (CDCL) SAT solvers using a variant of the VSIDS branching heuristic that solves instances of the Ordering Principle (OP) CNF formulas in time…
Modern Reinforcement Learning (RL) is more than just learning the optimal policy; Alternative learning goals such as exploring the environment, estimating the underlying model, and learning from preference feedback are all of practical…
Recent work introduced the cube-and-conquer technique to solve hard SAT instances. It partitions the search space into cubes using a lookahead solver. Each cube is tackled by a conflict-driven clause learning (CDCL) solver. Crucial for…
In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on…
In this paper, we consider the problem of deciding the existence of real solutions to a system of polynomial equations having real coefficients, and which are invariant under the action of the symmetric group. We construct and analyze a…
Sequential decision-making problems with multiple objectives arise naturally in practice and pose unique challenges for research in decision-theoretic planning and learning, which has largely focused on single-objective settings. This…
Projecting a vector onto a simplex is a well-studied problem that arises in a wide range of optimization problems. Numerous algorithms have been proposed for determining the projection; however, the primary focus of the literature has been…
We introduce a novel criterion in clustering that seeks clusters with limited range of values associated with each cluster's elements. In clustering or classification the objective is to partition a set of objects into subsets, called…
This paper presents a complete algorithmic study of the decision Boolean Satisfiability Problem under the classical computation and quantum computation theories. The paper depicts deterministic and probabilistic algorithms, propositions of…
When dealing with real-world optimization problems, decision-makers usually face high levels of uncertainty associated with partial information, unknown parameters, or complex relationships between these and the problem decision variables.…
Boolean satisfiability (SAT) solvers are widely used in hardware verification, cryptanalysis, automatic test-pattern generation, and side-channel reasoning workflows. Modern conflict-driven clause-learning (CDCL) solvers are highly…
We refine the formulation of the Boolean satisfiability problem with $n$ Boolean variables in Clifford algebra ${\cal C}\ell(\mathbb{R}^{n,n})$ [3] and exploit this continuous setting to outline a new unsatisfiability test. This algorithm…
We consider a class of stochastic programs whose uncertain data has an exponential number of possible outcomes, where scenarios are affinely parametrized by the vertices of a tractable binary polytope. Under these conditions, we propose a…
A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…
Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…