Abstract
Reactive synthesis holds the promise of generating automatically a verifiably correct program from a high-level specification. A popular such specification language is Linear Temporal Logic (LTL). Unfortunately, synthesizing programs from general LTL formulas, which relies on first constructing a game arena and then solving the game, does not scale to large instances. The specifications from practical applications are usually large conjunctions of smaller LTL formulas, which inspires existing compositional synthesis approaches to take advantage of this structural information. The main challenge here is that they solve the game only after obtaining the game arena, the most computationally expensive part in the procedure. In this work, we propose a compositional synthesis technique to tackle this difficulty by synthesizing a program for each small conjunct separately and composing them one by one. While this approach does not work for general LTL formulas, we show here that it does work for Safety LTL formulas, a popular and important fragment of LTL. While we have to compose all the programs of small conjuncts in the worst case, we can prune the intermediate programs to make later compositions easier and immediately conclude unrealizable as soon as some part of the specification is found unrealizable. By comparing our compositional approach with a portfolio of all other approaches, we observed that our approach was able to solve a notable number of instances not solved by others. In particular, experiments on scalable conjunctive benchmarks showed that our approach scale well and significantly outperform current Safety LTL synthesis techniques. We conclude that our compositional approach is an important contribution to the algorithmic portfolio of Safety LTL synthesis.
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References
Baier, C., Katoen, J.: Principles of Model Checking. MIT Press, Cambridge (2008)
Bansal, S., Li, Y., Tabajara, L.M., Vardi, M.Y.: Hybrid compositional reasoning for reactive synthesis from finite-horizon specifications. In: AAAI, pp. 9766–9774 (2020)
Bernet, J., Janin, D., Walukiewicz, I.: Permissive strategies: from parity games to safety games. RAIRO Theor. Inform. Appl. 36(3), 261–275 (2002)
Bloem, R., Jobstmann, B., Piterman, N., Pnueli, A., Sa’ar, Y.: Synthesis of reactive (1) designs. J. Comput. Syst. Sci. 78(3), 911–938 (2012)
Bohy, A., Bruyère, V., Filiot, E., Jin, N., Raskin, J.-F.: Acacia+, a tool for LTL synthesis. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 652–657. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31424-7_45
Chang, E., Manna, Z., Pnueli, A.: Characterization of temporal property classes. In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, pp. 474–486. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55719-9_97
Church, A.: Application of recursive arithmetic to the problem of circuit synthesis. J. Symb. Log. 28(4), 289–290 (1963)
Cimatti, A., Geatti, L., Gigante, N., Montanari, A., Tonetta, S.: Expressiveness of extended bounded response LTL. In: GandALF 2021, pp. 152–165 (2021)
De Giacomo, G., Favorito, M.: Compositional approach to translate LTL\(_f\)/LDL\(_f\) into deterministic finite automata. In: ICAPS, pp. 122–130 (2021)
Duret-Lutz, A., Lewkowicz, A., Fauchille, A., Michaud, T., Renault, É., Xu, L.: Spot 2.0—a framework for LTL and \(\omega \)-automata manipulation. In: Artho, C., Legay, A., Peled, D. (eds.) ATVA 2016. LNCS, vol. 9938, pp. 122–129. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46520-3_8
Ehlers, R., Raman, V.: Slugs: extensible GR(1) synthesis. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9780, pp. 333–339. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-41540-6_18
Esparza, J., Křetínský, J., Sickert, S.: From LTL to deterministic automata - a safraless compositional approach. Formal Methods Syst. Des. 49(3), 219–271 (2016)
Faymonville, P., Finkbeiner, B., Tentrup, L.: BoSy: an experimentation framework for bounded synthesis. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10427, pp. 325–332. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63390-9_17
Filiot, E., Jin, N., Raskin, J.: Antichains and compositional algorithms for LTL synthesis. Formal Methods Syst. Des. 39(3), 261–296 (2011). https://doi.org/10.1007/s10703-011-0115-3
Finkbeiner, B., Geier, G., Passing, N.: Specification decomposition for reactive synthesis. In: NFM, pp. 113–130 (2021)
Finkbeiner, B., Passing, N.: Dependency-based compositional synthesis. In: Hung, D.V., Sokolsky, O. (eds.) ATVA 2020. LNCS, vol. 12302, pp. 447–463. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-59152-6_25
Giacomo, G.D., Vardi, M.Y.: Linear temporal logic and linear dynamic logic on finite traces. In: IJCAI, pp. 854–860 (2013)
Henriksen, J.G., et al.: Mona: monadic second-order logic in practice. In: Brinksma, E., Cleaveland, W.R., Larsen, K.G., Margaria, T., Steffen, B. (eds.) TACAS 1995. LNCS, vol. 1019, pp. 89–110. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-60630-0_5
Kupferman, O., Piterman, N., Vardi, M.Y.: Safraless compositional synthesis. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 31–44. Springer, Heidelberg (2006). https://doi.org/10.1007/11817963_6
Kupferman, O., Vardi, M.Y.: Model checking of safety properties. Formal Methods Syst. Des. 19(3), 291–314 (2001). https://doi.org/10.1023/A:1011254632723
Kupferman, O., Vardi, M.Y.: Safraless decision procedures. In: FOCS, pp. 531–542 (2005)
Meyer, P.J., Sickert, S., Luttenberger, M.: Strix: explicit reactive synthesis strikes back! In: Chockler, H., Weissenbacher, G. (eds.) CAV 2018. LNCS, vol. 10981, pp. 578–586. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96145-3_31
Michaud, T., Colange, M.: Reactive synthesis from LTL specification with spot. In: SYNT@CAV (2018)
Plaku, E., Kavraki, L.E., Vardi, M.Y.: Falsification of LTL safety properties in hybrid systems. Int. J. Softw. Tools Technol. Transf. 15(4), 305–320 (2013). https://doi.org/10.1007/s10009-012-0233-2
Pnueli, A.: The temporal logic of programs. In: FOCS, pp. 46–57 (1977)
Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: POPL, pp. 179–190 (1989)
Sickert, S., Esparza, J.: An efficient normalisation procedure for linear temporal logic and very weak alternating automata. In: LICS, pp. 831–844 (2020)
Sistla, A.P.: Safety, liveness and fairness in temporal logic. Formal Aspects Comput. 6(5), 495–512 (1994). https://doi.org/10.1007/BF01211865
Sohail, S., Somenzi, F.: Safety first: a two-stage algorithm for the synthesis of reactive systems. Int. J. Softw. Tools Technol. Transf. 15(5–6), 433–454 (2013). https://doi.org/10.1007/s10009-012-0224-3
Somenzi, F.: CUDD: CU decision diagram package 3.0.0. University of Colorado at Boulder
Tabajara, L.M., Vardi, M.Y.: Partitioning techniques in LTL\(_f\) synthesis. In: IJCAI, pp. 5599–5606 (2019)
Vardi, M.Y.: From verification to synthesis. In: Shankar, N., Woodcock, J. (eds.) VSTTE 2008. LNCS, vol. 5295, p. 2. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-87873-5_2
Zhu, S., Tabajara, L.M., Li, J., Pu, G., Vardi, M.Y.: A symbolic approach to safety ltl synthesis. In: Strichman, O., Tzoref-Brill, R. (eds.) HVC 2017. LNCS, vol. 10629, pp. 147–162. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70389-3_10
Zhu, S., Tabajara, L.M., Li, J., Pu, G., Vardi, M.Y.: Symbolic LTL\(_f\) synthesis. In: IJCAI, pp. 1362–1369 (2017)
Zhu, S., Tabajara, L.M., Pu, G., Vardi, M.Y.: On the power of automata minimization in temporal synthesis. In: GandALF, pp. 117–134 (2021)
Acknowledgement
This work is supported in part by the ERC Advanced Grant WhiteMech (No. 834228), the EU ICT-48 2020 project TAILOR (No. 952215), the PRIN project RIPER (No. 20203FFYLK), the National Natural Science Foundation of China (Grant Nos. 62102407 and 61836005), CAS grant QYZDB-SSW-SYS019, NSF grants IIS-1527668, CCF-1704883, IIS-1830549, CNS-2016656, DoD MURI grant N00014-20-1-2787, and an award from the Maryland Procurement Office.
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Bansal, S., De Giacomo, G., Di Stasio, A., Li, Y., Vardi, M.Y., Zhu, S. (2023). Compositional Safety LTL Synthesis. In: Lal, A., Tonetta, S. (eds) Verified Software. Theories, Tools and Experiments.. VSTTE 2022. Lecture Notes in Computer Science, vol 13800. Springer, Cham. https://doi.org/10.1007/978-3-031-25803-9_1
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