[Paper Review] LTL to Büchi Automata Translation: Fast and More Deterministic

Tomáš Babiak, Mojmír Křetínský+2 more|arXiv (Cornell University)|Jan 3, 2012

Formal Methods in Verification13 references38 citations

TL;DR

This paper presents LTL3BA, an optimized LTL-to-Büchi automaton translator that improves upon LTL2BA by enhancing speed, reducing automaton size, and increasing determinism through algorithmic and implementation-level modifications. The key contribution is a new class of 'alternating' LTL formulae—those with both 'G' and 'F' operators on every syntax tree branch—whose validity is prefix-invariant, enabling performance gains; LTL3BA outperforms both LTL2BA and SPOT in speed while producing automata of comparable or better quality.

ABSTRACT

We introduce improvements in the algorithm by Gastin and Oddoux translating LTL formulae into Büchi automata via very weak alternating co-Büchi automata and generalized Büchi automata. Several improvements are based on specific properties of any formula where each branch of its syntax tree contains at least one eventually operator and at least one always operator. These changes usually result in faster translations and smaller automata. Other improvements reduce non-determinism in the produced automata. In fact, we modified all the steps of the original algorithm and its implementation known as LTL2BA. Experimental results show that our modifications are real improvements. Their implementations within an LTL2BA translation made LTL2BA very competitive with the current version of SPOT, sometimes outperforming it substantially.

Motivation & Objective

• Address the need for fast, high-quality LTL-to-Büchi automaton translations in model checking and satisfiability checking.
• Improve upon the long-standing LTL2BA tool, which had not seen major updates since 2007, despite SPOT's ongoing enhancements.
• Reduce non-determinism and automaton size while maintaining or improving translation speed.
• Introduce a novel class of LTL formulae—'alternating' formulae—whose validity is independent of finite word prefixes, enabling targeted optimizations.
• Demonstrate that high-quality automata can be generated quickly, supporting early vacuity checks and efficient model checking pipelines.

Proposed method

• Identify and exploit prefix-invariance in LTL formulae containing both 'G' (always) and 'F' (eventually) on every branch of their syntax tree, defining a new class of 'alternating' formulae.
• Modify each step of the LTL2BA pipeline: VWAA construction, TGBA translation, and BA degeneralization, using formula-specific optimizations.
• Apply formula reduction rules and simplify automata at each stage to reduce state and transition count.
• Introduce a generalized optimization for VWAA that reduces non-determinism in the initial automaton construction.
• Implement the new algorithm as LTL3BA, a public tool available under GPL, with performance tuned for speed and output quality.
• Leverage the prefix-invariance property to avoid redundant state exploration during VWAA and TGBA construction, especially in parametric formulae.

Experimental results

Research questions

• RQ1 Can we identify a syntactic class of LTL formulae for which validity is independent of finite word prefixes, enabling performance optimizations?
• RQ2 How can we modify the LTL2BA pipeline to improve translation speed, automaton size, and determinism without sacrificing correctness?
• RQ3 To what extent can prefix-invariant formulae be exploited to reduce state explosion in LTL-to-Büchi translations?
• RQ4 How does the performance and output quality of the new translator LTL3BA compare to LTL2BA and SPOT across diverse LTL formulae?
• RQ5 Can the new optimizations achieve minimal or near-minimal automata for challenging parametric formulae while remaining significantly faster than existing tools?

Key findings

• LTL3BA produces automata that are, on average, smaller and more deterministic than those from LTL2BA, with up to half the number of states and transitions for certain formulae.
• For the parametric formula θₙ, LTL3BA generates automata with roughly half the size of SPOT’s output, while being 8 times faster on average.
• On the benchmark set from Cichoń et al. (2009), LTL3BA computed minimal automata in under 2 minutes (95 seconds), compared to SPOT’s 13+ minutes (802 seconds).
• LTL3BA outperforms LTL2BA in speed for larger formulae, while remaining competitive with SPOT, especially on complex or parametric formulae.
• The prefix-invariance property of 'alternating' formulae enables significant performance gains, particularly in VWAA and TGBA construction stages.
• LTL3BA is faster than SPOT on small to medium formulae and remains competitive on larger ones, with output quality comparable to SPOT’s default settings.