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Minimality Notions via Factorization Systems ((Co)algebraic pearls)

Author Thorsten Wißmann

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Thorsten Wißmann
  • Radboud University Nijmegen, The Netherlands


The author thanks Stefan Milius and Jurriaan Rot for inspiring discussions and thanks the referees for their helpful comments.

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Thorsten Wißmann. Minimality Notions via Factorization Systems ((Co)algebraic pearls). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 24:1-24:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Coalgebra
  • Reachability
  • Observability
  • Minimization
  • Factorization System


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