Coalgebraic Determinization of Alternating Automata

TL;DR

This paper extends coalgebraic determinization to alternating automata, providing a unified, category-theoretic framework that aligns with concrete semantics and introduces a novel distributive law.

Contribution

It introduces a coalgebraic determinization method for alternating automata, solving an open problem by defining a key distributive law.

Findings

Successfully determinizes alternating automata coalgebraically

Ensures semantics coincide with concrete definitions

Provides a unified approach for various automata types

Abstract

Coalgebra is a currently quite active field, which aims to look at generic state-based systems (most prominently automata) from a very abstract point of view, mainly using tools from category theory. One of its achievements is to give a completely generic approach of determinization, unifying in an elegant manner non-deterministic automata, probabilistic automata or non-deterministic pushdown automata in one and the same model. However, the case of alternating automata fails to easily fit in this model. The aim of this internship was therefore to tackle this problem: can alternating automata also be determinized in the coalgebraic way? Does this give semantics that coincides with the concretely defined one? In this report, we give a positive answer to both questions. The main element of our construction is a distributive law, the definition of which has been for some time an open question.