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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence / EAAI-20

A SAT+CAS Approach to Finding Good Matrices: New Examples and Counterexamples

February 1, 2023

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Authors

Curtis Bright

University of Waterloo


Dragomir Ž. Ðoković

University of Waterloo


Ilias Kotsireas

Wilfrid Laurier University


Vijay Ganesh

University of Waterloo


DOI:

10.1609/aaai.v33i01.33011435


Abstract:

We enumerate all circulant good matrices with odd orders divisible by 3 up to order 70. As a consequence of this we find a previously overlooked set of good matrices of order 27 and a new set of good matrices of order 57. We also find that circulant good matrices do not exist in the orders 51, 63, and 69, thereby finding three new counterexamples to the conjecture that such matrices exist in all odd orders. Additionally, we prove a new relationship between the entries of good matrices and exploit this relationship in our enumeration algorithm. Our method applies the SAT+CAS paradigm of combining computer algebra functionality with modern SAT solvers to efficiently search large spaces which are specified by both algebraic and logical constraints.

Topics: AAAI

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HOW TO CITE:

Curtis Bright||Dragomir Ž. Ðoković||Ilias Kotsireas||Vijay Ganesh A SAT+CAS Approach to Finding Good Matrices: New Examples and Counterexamples Proceedings of the AAAI Conference on Artificial Intelligence (2019) 1435-1442.

Curtis Bright||Dragomir Ž. Ðoković||Ilias Kotsireas||Vijay Ganesh A SAT+CAS Approach to Finding Good Matrices: New Examples and Counterexamples AAAI 2019, 1435-1442.

Curtis Bright||Dragomir Ž. Ðoković||Ilias Kotsireas||Vijay Ganesh (2019). A SAT+CAS Approach to Finding Good Matrices: New Examples and Counterexamples. Proceedings of the AAAI Conference on Artificial Intelligence, 1435-1442.

Curtis Bright||Dragomir Ž. Ðoković||Ilias Kotsireas||Vijay Ganesh. A SAT+CAS Approach to Finding Good Matrices: New Examples and Counterexamples. Proceedings of the AAAI Conference on Artificial Intelligence 2019 p.1435-1442.

Curtis Bright||Dragomir Ž. Ðoković||Ilias Kotsireas||Vijay Ganesh. 2019. A SAT+CAS Approach to Finding Good Matrices: New Examples and Counterexamples. "Proceedings of the AAAI Conference on Artificial Intelligence". 1435-1442.

Curtis Bright||Dragomir Ž. Ðoković||Ilias Kotsireas||Vijay Ganesh. (2019) "A SAT+CAS Approach to Finding Good Matrices: New Examples and Counterexamples", Proceedings of the AAAI Conference on Artificial Intelligence, p.1435-1442

Curtis Bright||Dragomir Ž. Ðoković||Ilias Kotsireas||Vijay Ganesh, "A SAT+CAS Approach to Finding Good Matrices: New Examples and Counterexamples", AAAI, p.1435-1442, 2019.

Curtis Bright||Dragomir Ž. Ðoković||Ilias Kotsireas||Vijay Ganesh. "A SAT+CAS Approach to Finding Good Matrices: New Examples and Counterexamples". Proceedings of the AAAI Conference on Artificial Intelligence, 2019, p.1435-1442.

Curtis Bright||Dragomir Ž. Ðoković||Ilias Kotsireas||Vijay Ganesh. "A SAT+CAS Approach to Finding Good Matrices: New Examples and Counterexamples". Proceedings of the AAAI Conference on Artificial Intelligence, (2019): 1435-1442.

Curtis Bright||Dragomir Ž. Ðoković||Ilias Kotsireas||Vijay Ganesh. A SAT+CAS Approach to Finding Good Matrices: New Examples and Counterexamples. AAAI[Internet]. 2019[cited 2023]; 1435-1442.


ISSN: 2374-3468


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