To automate the discovery of conjectures on combinatorial objects, we introduce the concept of a map of sharp bounds on characteristics of combinatorial objects, that provides a set of interrelated sharp bounds for these combinatorial objects. We then describe a Bound Seeker, a CP-based system, that gradually acquires maps of conjectures. The system was tested for searching conjectures on bounds on characteristics of digraphs: it constructs sixteen maps involving 431 conjectures on sharp lower and upper-bounds on eight digraph characteristics.
@InProceedings{beldiceanu_et_al:LIPIcs.CP.2022.6, author = {Beldiceanu, Nicolas and Cheukam-Ngouonou, Jovial and Douence, R\'{e}mi and Gindullin, Ramiz and Quimper, Claude-Guy}, title = {{Acquiring Maps of Interrelated Conjectures on Sharp Bounds}}, booktitle = {28th International Conference on Principles and Practice of Constraint Programming (CP 2022)}, pages = {6:1--6:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-240-2}, ISSN = {1868-8969}, year = {2022}, volume = {235}, editor = {Solnon, Christine}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2022.6}, URN = {urn:nbn:de:0030-drops-166353}, doi = {10.4230/LIPIcs.CP.2022.6}, annote = {Keywords: Acquisition of conjectures, digraphs, bounds} }
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