Abstract
The synthesis problem asks for the automatic construction of a system from its specification. In the traditional setting, the system is “constructed from scratch” rather than composed from reusable components. However, this is rare in practice, and almost every non-trivial software system relies heavily on the use of libraries of reusable components. Recently, Lustig and Vardi introduced dataflow and controlflow synthesis from libraries of reusable components. They proved that dataflow synthesis is undecidable, while controlflow synthesis is decidable. The problem of controlflow synthesis from libraries of probabilistic components was considered by Nain, Lustig and Vardi, and was shown to be decidable for qualitative analysis (that asks that the specification be satisfied with probability 1). Our main contribution for controlflow synthesis from probabilistic components is to establish better complexity bounds for the qualitative analysis problem, and to show that the more general quantitative problem is undecidable. For the qualitative analysis, we show that the problem (i) is EXPTIME-complete when the specification is given as a deterministic parity word automaton, improving the previously known 2EXPTIME upper bound; and (ii) belongs to UP \(\cap \) coUP and is parity-games hard, when the specification is given directly as a parity condition on the components, improving the previously known EXPTIME upper bound.
This research was supported by Austrian Science Fund (FWF) Grant No P23499- N23, FWF NFN Grant No S11407-N23 (SHiNE), ERC Start grant (279307: Graph Games), EU FP7 Project Cassting, NSF grants CNS 1049862 and CCF-1139011, by NSF Expeditions in Computing project “ExCAPE: Expeditions in Computer Augmented Program Engineering”, by BSF grant 9800096, and by gift from Intel.
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References
Andersson, D., Miltersen, P.B.: The Complexity of Solving Stochastic Games on Graphs. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 112–121. Springer, Heidelberg (2009)
Avni, G., Kupferman, O.: Synthesis from Component Libraries with Costs. In: Baldan, P., Gorla, D. (eds.) CONCUR 2014. LNCS, vol. 8704, pp. 156–172. Springer, Heidelberg (2014)
Baier, C., Katoen, J.-P.: Principles of Model Checking (Representation and Mind Series). The MIT Press (2008)
Chatterjee, K.: Stochastic \(\omega \)-regular Games. PhD thesis, UC Berkeley (2007)
Chatterjee, K., Doyen, L., Nain, S., Vardi, M.Y.: The Complexity of Partial-Observation Stochastic Parity Games with Finite-Memory Strategies. In: Muscholl, A. (ed.) FOSSACS 2014 (ETAPS). LNCS, vol. 8412, pp. 242–257. Springer, Heidelberg (2014)
Chatterjee, K., Doyen, L., Vardi. M. Y.: The complexity of synthesis from probabilistic components. CoRR, abs/1502.04844 (2015)
Chatterjee, K., Henzinger, T.A.: Reduction of stochastic parity to stochastic mean-payoff games. IPL 106(1), 1–7 (2008)
Chatterjee, K., Jurdziński, M., Henzinger, T.A.: Quantitative stochastic parity games. In: SODA 2004, pp. 114–123 (2004)
Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. J. ACM 42(4), 857–907 (1995)
De Crescenzo, I., La Torre, S.: Modular Synthesis with Open Components. In: Abdulla, P.A., Potapov, I. (eds.) RP 2013. LNCS, vol. 8169, pp. 96–108. Springer, Heidelberg (2013)
de Alfaro, L., Henzinger, T.A.: Interface Theories for Component-Based Design. In: Henzinger, T.A., Kirsch, C.M. (eds.) EMSOFT 2001. LNCS, vol. 2211, pp. 148–165. Springer, Heidelberg (2001)
Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: Verification of Probabilistic Real-Time Systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011)
Lustig, Y., Vardi, M.Y.: Synthesis from Component Libraries. In: de Alfaro, L. (ed.) FOSSACS 2009. LNCS, vol. 5504, pp. 395–409. Springer, Heidelberg (2009)
Nain, S., Lustig, Y., Vardi, M.Y.: Synthesis from probabilistic components. LMCS 10(2) (2014)
Paz, A.: Introduction to probabilistic automata. Academic Press Inc. (1971)
Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: Proc. of POPL, pp. 179–190. ACM Press (1989)
Sifakis, J.: A framework for component-based construction extended abstract. In: SFEM 2005, pp. 293–300 (2005)
Vardi, M.Y.: Automatic verification of probabilistic concurrent finite-state systems. In: FOCS 1985, pp. 327–338 (1985)
Vardi, M.Y.: Probabilistic Linear-Time Model Checking: An Overview of the Automata-Theoretic Approach. In: Katoen, J.-P. (ed.) AMAST-ARTS 1999, ARTS 1999, and AMAST-WS 1999. LNCS, vol. 1601, pp. 265–276. Springer, Heidelberg (1999)
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Chatterjee, K., Doyen, L., Vardi, M.Y. (2015). The Complexity of Synthesis from Probabilistic Components. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47666-6_9
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