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

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

May 02, 2023 107 likes •211 views

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

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LTL realizability and synthesis Theoretical background Acacia+ References

Acacia+, a Tool for LTL Synthesis

Aaron Bohy1 V´ eronique Bruy` ere1 Emmanuel Filiot2 Naiyong Jin3 Jean-Fran¸ cois Raskin2

1Universit´

e de Mons

2Universit´

e Libre de Bruxelles

3Synopsys, Shanghai

Computer Aided Verification (CAV) 2012

Berkeley, California, USA

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LTL realizability and synthesis Theoretical background Acacia+ 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 IO 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 ok ⊆ O
  • Player I responds by giving ik ⊆ I
  • Outcome of the game: w = (i1∪o1)(i2∪o2). . . (ik∪ok). . .
  • Player O wins the play if w satisfies φ, otherwise Player I wins
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LTL realizability and synthesis Theoretical background Acacia+ 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

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LTL realizability and synthesis Theoretical background Acacia+ 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 = φ1 ∧ . . . ∧ φn
  • Realizability and unrealizability check
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LTL realizability and synthesis Theoretical background Acacia+ 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

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LTL realizability and synthesis Theoretical background Acacia+ 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

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LTL realizability and synthesis Theoretical background Acacia+ References

Web page

Available at http://lit2.ulb.ac.be/acaciaplus/

Thank you! Questions?

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LTL realizability and synthesis Theoretical background Acacia+ 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.

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LTL realizability and synthesis Theoretical background Acacia+ 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