Document type
Journal articles
Document subtype
Full paper
Title
Disjunctive sums of quasi-nimbers
Participants in the publication
Alexandre Silva (Author)
Carlos Pereira dos Santos (Author)
João Pedro Neto (Author)
Dep. Informática
LASIGE
Richard J. Nowakowski (Author)
Summary
PAINT can is an example of a game whose positions are disjunctive sums, and a move in any component reduces that component to a nimber. Conway, in On Numbers and Games, partially analysed the related game supernim, and called these components “superstars”, mentioning “There does not appear to be a complete theory”. The book contains one result about these games, and, until now, there has been no advance in finding good strategies. Here, we show that, for a human, the use of canonical forms is not a good approach. We present an algorithmic, recursive approach to the general case, based on a fundamental reduction of these positions, as well as on a Nimber Avoidance Theorem. An analysis of the computational time of the algorithm is presented.
Date of Publication
2022-12
Where published
Theoretical Computer Science
Publication Identifiers
Publisher
Elsevier BV
Document Identifiers
DOI -
https://doi.org/10.1016/j.tcs.2022.12.015
URL -
http://dx.doi.org/10.1016/j.tcs.2022.12.015
URL -
https://doi.org/10.1016/j.tcs.2022.12.015
URL -
https://www.sciencedirect.com/science/article/pii/S030439752200737X?via%3Dihub
Rankings
SCIMAGO Q2 (2022) - 0.62 -
SCOPUS (2022) - 1.291
Google Metrics (2022) - 35