2026-07-24T08:33:51Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:15379 2024-03-06T10:55:16Z ddc:004 open_access

Minimality Notions via Factorization Systems ((Co)algebraic pearls) Wißmann, Thorsten Coalgebra Reachability Observability Minimization Factorization System For the minimization of state-based systems (i.e. the reduction of the number of states while retaining the system’s semantics), there are two obvious aspects: removing unnecessary states of the system and merging redundant states in the system. In the present article, we relate the two aspects on coalgebras by defining an abstract notion of minimality. The abstract notion minimality and minimization live in a general category with a factorization system. We will find criteria on the category that ensure uniqueness, existence, and functoriality of the minimization aspects. The proofs of these results instantiate to those for reachability and observability minimization in the standard coalgebra literature. Finally, we will see how the two aspects of minimization interact and under which criteria they can be sequenced in any order, like in automata minimization. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Thorsten Wißmann 2021 Is Part Of LIPIcs, Volume 211, 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CALCO.2021.24 urn:nbn:de:0030-drops-153791 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.24 eng https://creativecommons.org/licenses/by/4.0/legalcode