On the Minimisation of Deterministic and History-Deterministic Generalised (co)B\"uchi Automata

TL;DR

This paper introduces a polynomial-time minimisation algorithm for history-deterministic generalised coBüchi automata and proves NP-completeness for minimising deterministic and history-deterministic generalised Büchi automata.

Contribution

It provides the first polynomial-time algorithm for minimising history-deterministic generalised coBüchi automata and establishes NP-completeness results for related minimisation problems.

Findings

Polynomial-time algorithm for history-deterministic generalised coBüchi automata minimisation.

NP-completeness of minimising deterministic and history-deterministic generalised Büchi automata.

Complexity results for combined minimisation of states and colours.

Abstract

We present a polynomial-time algorithm minimising the number of states of history-deterministic generalised coB\"uchi automata, building on the work of Abu Radi and Kupferman on coB\"uchi automata. On the other hand, we establish that the minimisation problem for both deterministic and history-deterministic generalised B\"uchi automata is NP-complete, as well as the problem of minimising at the same time the number of states and colours of history-deterministic generalised coB\"uchi automata.