Reykjavik UniversityHáskólinn í ReykjavíkCapobianco, SilvioUustalu, Tarmo2024-02-292024-02-292023-10-22S. Capobianco, T. Uustalu. Additive cellular automata graded-monadically. In 25th International Symposium on Principles and Practice of Declarative Programming (PPDP ’23), October 22-23, 2023, Lisbon, Portugal, art. 13, 9 pp. ACM, New York, 2023. doi:10.1145/3610612.3610625979-8-4007-0812-1https://hdl.handle.net/20.500.11815/4744Cellular automata are an archetypical comonadic notion of computation in that computation happens in the coKleisli category of a comonad. In this paper, we show that they can also be viewed as graded comonadic—a perspective that turns out to be both more informative and also more basic. We also discuss additive cellular automata to show that they admit both a graded comonadic and a graded monadic view. That these two perspectives are simultaneously available in this special case arises from a graded version of an observation by Kleiner about adjoint comonad-monad pairs.article 13eninfo:eu-repo/semantics/closedAccessmodels of computationcellular automataadditive cellular automatacomonadsadjoint comonad-monad pairsgraded comonadsgraded monadsinfo:eu-repo/semantics/bookPart25th International Symposium on Principles and Practice of Declarative Programming (PPDP '23)10.1145/3610612.3610625