Formal Methods in System Design

, Volume 49, Issue 3, pp 219–271 | Cite as

From LTL to deterministic automata

A safraless compositional approach
  • Javier Esparza
  • Jan KřetínskýEmail author
  • Salomon Sickert


We present a new algorithm to construct a (generalized) deterministic Rabin automaton for an LTL formula \(\varphi \). The automaton is the product of a co-Büchi automaton for \(\varphi \) and an array of Rabin automata, one for each \({\mathbf {G}}\)-subformula of \(\varphi \). The Rabin automaton for \({\mathbf {G}}\psi \) is in charge of recognizing whether \({\mathbf {F}}{\mathbf {G}}\psi \) holds. This information is passed to the co-Büchi automaton that decides on acceptance. As opposed to standard procedures based on Safra’s determinization, the states of all our automata have a clear logical structure, which allows for various optimizations. Experimental results show improvement in the sizes of the resulting automata compared to existing methods.


Automata theory Temporal logic Verification 



We are grateful to the anonymous referees for their helpful comments to improve previous versions of the manuscript and their interesting suggestions for future work. This research was funded in part by the Czech Science Foundation Grant No. P202/12/G061, the DFG Research Training Group “PUMA: Programm- und Modell-Analyse” (GRK 1480), and the DFG grant CAVA, Computer Aided Verification of Automata.


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Fakultät für InformatikTechnische Universität MünchenGarching bei MünchenGermany

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