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Carlos Barrón-Romero

Publications and source records attributed to Carlos Barrón-Romero.

7 recordsLinked to original sources
arXiv2018

A novel algorithm for solving the Decision Boolean Satisfiability Problem without algebra

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 operations: expansion and simplification are used to explains why using algebra grows the resolution steps. It is proved that its complexity has an upper bound of $2^{n-1}$ where $n$ is the number of logical variables of the given problem.

cs.DS↗
arXiv2018

The fast parallel algorithm for CNF SAT without algebra

A novel parallel algorithm for solving the classical Decision Boolean Satisfiability problem with clauses in conjunctive normal form is depicted. My approach for solving SAT is without using algebra or other computational search strategies such as branch and bound, back-forward, tree representation, etc. The method is based on the special class of SAT problems, Simple SAT (SSAT). The algorithm's design includes parallel execution, object oriented, and short termination as my previous versions but it keep track of the tested unsatisfactory binary values to improve the efficiency and to favor short termination. The resulting algorithm is linear with respect to the number of clauses plus a process data on the partial solutions of the subproblems SSAT of an arbitrary SAT and it is bounded by $2^{n}$ iterations where $n$ is the number of logical variables. The novelty for the solution of arbitrary SAT problems is a linear algorithm, such its complexity is less or equal than the algorithms of the state of the art for solving SAT.

cs.DS↗
arXiv2017

Discrete Optimal Global Convergence of an Evolutionary Algorithm for Clusters under the Potential of Lennard Jones

A review of the properties that bond the particles under Lennard Jones Potential allow to states properties and conditions for building evolutive algorithms using the CB lattice with other different lattices. The new lattice is called CB lattice and it is based on small cubes. A set of propositions states convergence and optimal conditions over the CB lattice for an evolutionary algorithm. The evolutionary algorithm is a reload version of previous genetic algorithms based in phenotypes. The novelty using CB lattice, together with the other lattices, and ad-hoc cluster segmentation and enumeration, is to allow the combination of genotype (DNA coding for cluster using their particle's number) and phenotype (geometrical shapes using particle's coordinates in 3D). A parallel version of an evolutionary algorithm for determining the global optimality is depicted. The results presented are from a standalone program for a personal computer of the evolutionary algorithm, which can estimate all putative optimal Lennard Jones Clusters from 13 to 1612 particles. The novelty are the theoretical results for the evolutionary algorithm's efficiency, the strategies with phenotype or genotype, and the classification of the clusters based in an ad-hoc geometric algorithm for segmenting a cluster into its nucleus and layers. Also, the standalone program is not only capable to replicate the optimal Lennard Jones clusters in The Cambridge Cluster Database (CCD), but to find new ones.

cs.CE↗
arXiv2016

Lower bound for the Complexity of the Boolean Satisfiability Problem

This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery for an extreme case is presented to determine a stable complexity around $2^n$. The reformulation point out that the decision Boolean Satisfiability Problem can only be solved in exponential time. This implies there is not an efficient algorithm for the NP Class.

cs.CC↗
arXiv2016

Complexity and Stop Conditions for NP as General Assignment Problems, the Travel Salesman Problem in $\mathbb{R}^2$, Knight Tour Problem and Boolean Satisfiability Problem

This paper presents stop conditions for solving General Assignment Problems (GAP), in particular for Travel Salesman Problem in an Euclidian 2D space the well known condition Jordan's simple curve and opposite condition for the Knight Tour Problem. The Jordan's simple curve condition means that a optimal trajectory must be simple curve, i.e., without crossing but for Knight Tour Problem we use the contrary, the feasible trajectory must have crossing in all cities of the tour. The paper presents the algorithms, examples and some results come from Concorde's Home page. Several problem are studied to depict their properties. A classical decision problem SAT is studied in detail.

cs.DS↗
arXiv2016

Classical and Quantum Algorithms for the Boolean Satisfiability Problem

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 their properties and the main result is that the problem has not an efficient algorithm (NP is not P). Novel quantum algorithms and propositions depict that the complexity by quantum computation approach for solving the Boolean Satisfiability Problem or any NP problem is lineal time.

cs.CC↗