On the Power of Automata Minimization in Reactive Synthesis

TL;DR

This paper investigates automata minimization algorithms, specifically Hopcroft and Brzozowski, applied to LTLf formulas in reactive synthesis, demonstrating that Hopcroft's algorithm generally outperforms Brzozowski's in this context.

Contribution

The study provides a detailed comparison of two classical automata minimization algorithms applied to LTLf formulas, revealing the practical superiority of Hopcroft's algorithm in reactive synthesis.

Findings

Hopcroft's algorithm outperforms Brzozowski's when applied to LTLf automata in reactive synthesis.

Starting from LTLf formulas, Hopcroft's algorithm is the preferred minimization method.

Brzozowski's algorithm does not show practical advantages in this context.

Abstract

Temporal logic is often used to describe temporal properties in AI applications. The most popular language for doing so is Linear Temporal Logic (LTL). Recently, LTL on finite traces, LTLf, has been investigated in several contexts. In order to reason about LTLf, formulas are typically compiled into deterministic finite automata (DFA), as the intermediate semantic representation. Moreover, due to the fact that DFAs have canonical representation, efficient minimization algorithms can be applied to maximally reduce DFA size, helping to speed up subsequent computations. Here, we present a thorough investigation on two classical minimization algorithms, namely, the Hopcroft and Brzozowski algorithms. More specifically, we show how to apply these algorithms to semi-symbolic (explicit states, symbolic transition functions) automata representation. We then compare the two algorithms in the context of an LTLf-synthesis framework, starting from LTLf formulas. While earlier studies on comparing the two algorithms starting from randomly-generated automata concluded that neither algorithm dominates, our results suggest that starting from LTLf formulas, Hopcroft's algorithm is the best choice in the context of reactive synthesis. Deeper analysis explains why the supposed advantage of Brzozowski's algorithm does not materialize in practice.