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First-Order vs. Second-Order Encodings for \(\textsc {ltl}_f\)-to-Automata Translation

  • Shufang Zhu
  • Geguang PuEmail author
  • Moshe Y. Vardi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11436)

Abstract

Translating formulas of Linear Temporal Logic (ltl) over finite traces, or \({\textsc {ltl}}_f\), to symbolic Deterministic Finite Automata (DFA) plays an important role not only in \({\textsc {ltl}}_f\) synthesis, but also in synthesis for Safety ltl formulas. The translation is enabled by using \(\mathsf {MONA}\), a powerful tool for symbolic, BDD-based, DFA construction from logic specifications. Recent works used a first-order encoding of \({\textsc {ltl}}_f\) formulas to translate \({\textsc {ltl}}_f\) to First Order Logic (fol), which is then fed to \(\mathsf {MONA}\) to get the symbolic DFA. This encoding was shown to perform well, but other encodings have not been studied. Specifically, the natural question of whether second-order encoding, which has significantly simpler quantificational structure, can outperform first-order encoding remained open.

In this paper we address this challenge and study second-order encodings for \({\textsc {ltl}}_f\) formulas. We first introduce a specific mso encoding that captures the semantics of \({\textsc {ltl}}_f\) in a natural way and prove its correctness. We then explore is a Compact mso encoding, which benefits from automata-theoretic minimization, thus suggesting a possible practical advantage. To that end, we propose a formalization of symbolic DFA in second-order logic, thus developing a novel connection between BDDs and mso. We then show by empirical evaluations that the first-order encoding does perform better than both second-order encodings. The conclusion is that first-order encoding is a better choice than second-order encoding in \({\textsc {ltl}}_f\)-to-Automata translation.

Notes

Acknowledgments

Work supported in part by China HGJ Project No. 2017ZX01038102-002, NSFC Projects No. 61572197, No. 61632005 and No. 61532019, NSF grants IIS-1527668, IIS-1830549, and by NSF Expeditions in Computing project “ExCAPE: Expeditions in Computer Augmented Program Engineering”. Special thanks to Jeffrey M. Dudek and Dror Fried for useful discussions.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.East China Normal UniversityShanghaiChina
  2. 2.Rice UniversityHoustonUSA

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