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06/23/2023
A SAT Solver and Computer Algebra Attack on the Minimum Kochen-Specker Problem
One of the fundamental results in quantum foundations is the Kochen-Spec...
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01/26/2023
A New Lower Bound in the abc Conjecture
We prove that there exist infinitely many coprime numbers a, b, c with a...
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03/19/2021
Integer and Constraint Programming Revisited for Mutually Orthogonal Latin Squares
In this paper we provide results on using integer programming (IP) and c...
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12/08/2020
A SAT-based Resolution of Lam's Problem
In 1989, computer searches by Lam, Thiel, and Swiercz experimentally res...
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01/31/2020
Nonexistence Certificates for Ovals in a Projective Plane of Order Ten
In 1983, a computer search was performed for ovals in a projective plane...
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01/31/2020
Unsatisfiability Proofs for Weight 16 Codewords in Lam's Problem
In the 1970s and 1980s, searches performed by L. Carter, C. Lam, L. Thie...
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11/11/2019
A Nonexistence Certificate for Projective Planes of Order Ten with Weight 15 Codewords
Using techniques from the fields of symbolic computation and satisfiabil...
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07/27/2019
Complex Golay Pairs up to Length 28: A Search via Computer Algebra and Programmatic SAT
We use techniques from the fields of computer algebra and satisfiability...
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07/11/2019
The SAT+CAS Method for Combinatorial Search with Applications to Best Matrices
In this paper, we provide an overview of the SAT+CAS method that combine...
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07/09/2019
SAT Solvers and Computer Algebra Systems: A Powerful Combination for Mathematics
Over the last few decades, many distinct lines of research aimed at auto...
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06/14/2019
Effective problem solving using SAT solvers
In this article we demonstrate how to solve a variety of problems and pu...
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05/01/2019
New Infinite Families of Perfect Quaternion Sequences and Williamson Sequences
We present new constructions for perfect and odd perfect sequences over ...
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11/13/2018
A SAT+CAS Approach to Finding Good Matrices: New Examples and Counterexamples
We enumerate all circulant good matrices with odd orders divisible by 3 ...
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05/14/2018
Enumeration of Complex Golay Pairs via Programmatic SAT
We provide a complete enumeration of all complex Golay pairs of length u...
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04/03/2018
Applying Computer Algebra Systems with SAT Solvers to the Williamson Conjecture
We employ tools from the fields of symbolic computation and satisfiabili...
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04/03/2018