LIPIcs - Leibniz International Proceedings in Informatics. 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Doi
Abstract
We introduce arboreal categories, which have an intrinsic process structure, allowing dynamic notions
such as bisimulation and back-and-forth games, and resource notions such as number of rounds of
a game, to be defined. These are related to extensional or “static” structures via arboreal covers,
which are resource-indexed comonadic adjunctions. These ideas are developed in a very general,
axiomatic setting, and applied to relational structures, where the comonadic constructions for
pebbling, Ehrenfeucht-Fraïssé and modal bisimulation games recently introduced in [1, 5, 6] are
recovered, showing that many of the fundamental notions of finite model theory and descriptive
complexity arise from instances of arboreal covers