Determinization and Limit-determinization of Emerson-Lei automata

TL;DR

This paper introduces new methods for determinizing transition-based Emerson-Lei automata, including a product-based approach, and demonstrates that limit-determinization can be achieved with single-exponential complexity, enabling applications in probabilistic model checking.

Contribution

The paper presents three novel translation techniques from TELA to GBA, a new determinization method combining multiple GBA, and shows limit-determinization with single-exponential complexity.

Findings

Product approach is competitive with existing methods.

Limit-determinization has single-exponential blow-up.

Good-for-MDP automata enable probabilistic model checking.

Abstract

We study the problem of determinizing $\omega$-automata whose acceptance condition is defined on the transitions using Boolean formulas, also known as transition-based Emerson-Lei automata (TELA). The standard approach to determinize TELA first constructs an equivalent generalized B\"uchi automaton (GBA), which is later determinized. We introduce three new ways of translating TELA to GBA. Furthermore, we give a new determinization construction which determinizes several GBA separately and combines them using a product construction. An experimental evaluation shows that the product approach is competitive when compared with state-of-the-art determinization procedures. We also study limit-determinization of TELA and show that this can be done with a single-exponential blow-up, in contrast to the known double-exponential lower-bound for determinization. Finally, one version of the limit-determinization procedure yields good-for-MDP automata which can be used for quantitative probabilistic model checking.