Acacia + , a Tool for LTL Synthesis Aaron Bohy 1 ere 1 Emmanuel - PowerPoint PPT Presentation

Acacia+ LTL realizability and synthesis Theoretical background References Acacia + , a Tool for LTL Synthesis Aaron Bohy 1 ere 1 Emmanuel Filiot 2 V´ eronique Bruy` Naiyong Jin 3 cois Raskin 2 Jean-Fran¸ 1 Universit´ 2 Universit´ 3 Synopsys, Shanghai e de Mons e Libre de Bruxelles Computer Aided Verification (CAV) 2012 Berkeley, California, USA

Acacia+ LTL realizability and synthesis Theoretical background References Problems Linear Temporal Logic (LTL) Class of propositional logic extended with temporal operators ( X , U , ♦ , � ) Let φ be an LTL formula over the set I � O of atomic signals Realizability game • 2-player game: • Player O , the system, controls the set O • Player I , the environment, controls the set I • Infinite play: at each round k , • Player O gives a subset o k ⊆ O • Player I responds by giving i k ⊆ I • Outcome of the game: w = ( i 1 ∪ o 1 )( i 2 ∪ o 2 ) . . . ( i k ∪ o k ) . . . • Player O wins the play if w satisfies φ , otherwise Player I wins

Acacia+ LTL realizability and synthesis Theoretical background References Problems LTL realizability problem Decide whether the system has a winning strategy to satisfy φ against any strategy of the environment LTL synthesis problem Produce such a winning strategy when φ is realizable Theorem [Ros92]: The LTL realizability problem is 2ExpTime-Complete

Acacia+ LTL realizability and synthesis Theoretical background References Implemented method Method proposed in: 1. E. Filiot, N. Jin, and J.-F. Raskin. An antichain algorithm for LTL realizability. In Computer Aided Verification, CAV , volume 5643 of LNCS , pages 263-277. Springer, 2009. 2. E. Filiot, N. Jin, and J.-F. Raskin. Compositional algorithms for LTL synthesis. In Automated Technology for Verification and Analysis, ATVA , volume 6252 of LNCS , pages 112-127. Springer, 2010. Characteristics: • Handles full LTL • Safraless procedure • Reduction to safety games • Based on antichains • Compositional approach for φ = φ 1 ∧ . . . ∧ φ n • Realizability and unrealizability check

Acacia+ LTL realizability and synthesis Theoretical background References Acacia + Programming languages: • C : costly low level operations • Python : orchestration of these operations No BDDs but antichains Code is open and can be used, extended or adapted by the research community Web interface for convenience

Acacia+ LTL realizability and synthesis Theoretical background References Performance and application Acacia + against Lily [JB06] and Unbeast [Ehl10] on several benchmarks: • Time comparison: better or similar to other tools • Able to handle large formulas (compositional approach) • Synthetizes compact strategies (Moore machines) Application scenarios: • Controller synthesis from LTL specifications • Debugging of LTL specifications • From LTL to Deterministic B¨ uchi Automata (DBA) • Size of the constructed automata very close to that of minimum DBA • Minimum DBA obtained for 18/26 formulas ⇒ Hope to see you all on Thursday

Acacia+ LTL realizability and synthesis Theoretical background References Web page Available at http://lit2.ulb.ac.be/acaciaplus/ Thank you! Questions?

Acacia+ LTL realizability and synthesis Theoretical background References R. Ehlers. Symbolic bounded synthesis. In CAV , volume 6174 of LNCS , pages 365–379. Springer Verlag, 2010. E. Filiot, N. Jin, and J.-F. Raskin. An antichain algorithm for LTL realizability. In CAV , volume 5643 of LNCS , pages 263–277. Springer, 2009. E. Filiot, N. Jin, and J.-F. Raskin. Compositional algorithms for LTL synthesis. In ATVA , pages 112–127, 2010. B. Jobstmann and R. Bloem. Optimizations for LTL synthesis. In FMCAD , pages 117–124, 2006. O. Kupferman and M. Y. Vardi. Safraless decision procedures. In FOCS , pages 531–542, 2005. R. Rosner. Modular synthesis of reactive systems. Ph.d. dissertation, Weizmann Institute of Science, 1992.

Acacia+ LTL realizability and synthesis Theoretical background References From LTL to Deterministic B¨ uchi Automata Idea from [KV05]: • Let φ be an LTL formula defined over P and σ �∈ P • Let I = P and O = { σ } • Then ( φ ↔ �♦ σ ) is realizable ⇔ there exists a DBA equivalent to φ In pratice: • Size of the constructed automata very close to that of minimum DBA • Minimum DBA obtained for 18/26 formulas