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Antichains and compositional algorithms for LTL synthesis

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Abstract

In this paper, we present new monolithic and compositional algorithms to solve the LTL realizability problem. Those new algorithms are based on a reduction of the LTL realizability problem to a game whose winning condition is defined by a universal automaton on infinite words with a k-co-Büchi acceptance condition. This acceptance condition asks that runs visit at most k accepting states, so it implicitly defines a safety game. To obtain efficient algorithms from this construction, we need several additional ingredients. First, we study the structure of the underlying automata constructions, and we show that there exists a partial order that structures the state space of the underlying safety game. This partial order can be used to define an efficient antichain algorithm. Second, we show that the algorithm can be implemented in an incremental way by considering increasing values of k in the acceptance condition. Finally, we show that for large LTL formulas that are written as conjunctions of smaller formulas, we can solve the problem compositionally by first computing winning strategies for each conjunct that appears in the large formula. We report on the behavior of those algorithms on several benchmarks. We show that the compositional algorithms are able to handle LTL formulas that are several pages long.

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Authors and Affiliations

  1. Département d’Informatique, Université Libre de Bruxelles, Bld du Triomphe, CP 212, 1050, Brussels, Belgium

    Emmanuel Filiot, Naiyong Jin & Jean-François Raskin

Authors
  1. Emmanuel Filiot
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  2. Naiyong Jin
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  3. Jean-François Raskin
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Corresponding author

Correspondence to Emmanuel Filiot.

Additional information

This paper extends the results of the two following previous papers [10, 11] by the authors.

Work supported by the projects: (i) QUASIMODO (FP7-ICT-STREP-214755), Quasimodo: “Quantitative System Properties in Model-Driven-Design of Embedded”, http://www.quasimodo.aau.dk/, (ii) GASICS (ESF-EUROCORES LogiCCC), Gasics: “Games for Analysis and Synthesis of Interactive Computational Systems”, http://www.ulb.ac.be/di/gasics/, (iii) Moves: “Fundamental Issues in Modelling, Verification and Evolution of Software”, http://moves.ulb.ac.be, a PAI program funded by the Federal Belgian Gouvernment, and (iv) ECSPER (ANR-JC09-472677) and SFINCS (ANR-07-SESU-012), two projects supported by the French National Research Agency.

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Filiot, E., Jin, N. & Raskin, JF. Antichains and compositional algorithms for LTL synthesis. Form Methods Syst Des 39, 261–296 (2011). https://doi.org/10.1007/s10703-011-0115-3

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