scholarly journals Unsatisfiability Proofs for Weight 16 Codewords in Lam's Problem

2020 ◽  
Author(s):  
Curtis Bright ◽  
Kevin K.H. Cheung ◽  
Brett Stevens ◽  
Ilias Kotsireas ◽  
Vijay Ganesh
Keyword(s):  
Symmetry Breaking ◽  
Computer Algebra ◽  
Computer Algebra System ◽  
Computing Time ◽  
Projective Planes ◽  
Computer Programs ◽  
Boolean Satisfiability ◽  
Sat Solving ◽  
Boolean Satisfiability Problem ◽  
C Program

In the 1970s and 1980s, searches performed by L. Carter, C. Lam, L. Thiel, and S. Swiercz showed that projective planes of order ten with weight 16 codewords do not exist. These searches required highly specialized and optimized computer programs and required about 2,000 hours of computing time on mainframe and supermini computers. In 2010, these searches were verified by D. Roy using an optimized C program and 16,000 hours on a cluster of desktop machines. We performed a verification of these searches by reducing the problem to the Boolean satisfiability problem (SAT). Our verification uses the cube-and-conquer SAT solving paradigm, symmetry breaking techniques using the computer algebra system Maple, and a result of Carter that there are ten nonisomorphic cases to check. Our searches completed in about 30 hours on a desktop machine and produced nonexistence proofs of about 1 terabyte in the DRAT (deletion resolution asymmetric tautology) format.

Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

1998 ◽  
Vol 37 (03) ◽  
pp. 235-238 ◽  
Author(s):  
M. El-Taha ◽  
D. E. Clark
Keyword(s):  
Monte Carlo ◽  
Decision Trees ◽  
Computer Algebra ◽  
Taylor Series ◽  
Computer Algebra System ◽  
Random Variable ◽  
Monte Carlo Analysis ◽  
Normal Random Variable ◽  
Medical Decision ◽  
Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

The Maple computer algebra system: A review

1995 ◽  
Vol 10 (3) ◽  
pp. 329-337 ◽  
Author(s):  
John Hutton ◽  
James Hutton
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
System A

scholarly journals The Computational Complexity of Probabilistic Planning

1998 ◽  
Vol 9 ◽  
pp. 1-36 ◽  
Author(s):  
M. L. Littman ◽  
J. Goldsmith ◽  
M. Mundhenk
Keyword(s):  
Computational Complexity ◽  
Efficient Algorithms ◽  
Boolean Satisfiability ◽  
Complexity Classes ◽  
Probabilistic Planning ◽  
Plan Evaluation ◽  
Partially Ordered ◽  
Boolean Satisfiability Problem ◽  
Complete Problem ◽  
Planning Problems

We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought; we examine totally ordered plans, acyclic plans, and looping plans, and partially ordered plans under three natural definitions of plan value. We show that problems of interest are complete for a variety of complexity classes: PL, P, NP, co-NP, PP, NP^PP, co-NP^PP, and PSPACE. In the process of proving that certain planning problems are complete for NP^PP, we introduce a new basic NP^PP-complete problem, E-MAJSAT, which generalizes the standard Boolean satisfiability problem to computations involving probabilistic quantities; our results suggest that the development of good heuristics for E-MAJSAT could be important for the creation of efficient algorithms for a wide variety of problems.

scholarly journals OPTIMALISASI MOTIVASI DAN PRESTASI BELAJAR MENGGUNAKAN MOODLE BERBANTUAN COMPUTER ALGEBRA SYSTEM (CAS)

2020 ◽  
Vol 9 (1) ◽  
pp. 53
Author(s):  
Kamhar Ngado ◽  
Rosnawati Rosnawati ◽  
Heri Retnawati ◽  
Sri Andayani
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System

scholarly journals Generation of equations for shell models of turbulence in the Maple system

2021 ◽  
Vol 254 ◽  
pp. 02006
Author(s):  
Liubov Feshchenko ◽  
Gleb Vodinchar
Keyword(s):  
Computer Algebra ◽  
Power Law ◽  
Computer Algebra System ◽  
Nonlinear Interactions ◽  
Systems Of Equations ◽  
Shell Models ◽  
Quadratic Invariants ◽  
Automated Compilation ◽  
Shell Models Of Turbulence

The paper describes a technology for the automated compilation of equations for shell models of turbulence in the computer algebra system Maple. A general form of equations for the coefficients of nonlinear interactions is given, which will ensure that the required combination of quadratic invariants and power-law solutions is fulfilled in the model. Described the codes for the Maple system allowing to generate and solve systems of equations for the coefficients. The proposed technology allows you to quickly and accurately generate classes of shell models with the desired properties.

Sign in / Sign up

Export Citation Format

Share Document