Thorsten Wißmann - Minimality Notions via Factorization Systems and Examples

lmcs:9893 - Logical Methods in Computer Science, September 8, 2022, Volume 18, Issue 3 -
Minimality Notions via Factorization Systems and Examples

Authors: Thorsten Wißmann

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 minimization aspects on coalgebras by defining an abstract notion of minimality. The abstract notions 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.

Volume: Volume 18, Issue 3
Published on: September 8, 2022
Accepted on: August 11, 2022
Submitted on: August 5, 2022
Keywords: Computer Science - Formal Languages and Automata Theory