Article

Better Quality in Synthesis through Quantitative Objectives

Authors:

Roderick Bloem,

Krishnendu Chatterjee,

Thomas A. Henzinger,

Barbara JobstmannAuthors Info & Claims

CAV '09: Proceedings of the 21st International Conference on Computer Aided Verification

Pages 140 - 156

https://doi.org/10.1007/978-3-642-02658-4_14

Published: 23 June 2009 Publication History

Abstract

Most specification languages express only qualitative constraints. However, among two implementations that satisfy a given specification, one may be preferred to another. For example, if a specification asks that every request is followed by a response, one may prefer an implementation that generates responses quickly but does not generate unnecessary responses. We use quantitative properties to measure the "goodness" of an implementation. Using games with corresponding quantitative objectives, we can synthesize "optimal" implementations, which are preferred among the set of possible implementations that satisfy a given specification.

In particular, we show how automata with lexicographic mean-payoff conditions can be used to express many interesting quantitative properties for reactive systems. In this framework, the synthesis of optimal implementations requires the solution of lexicographic mean-payoff games (for safety requirements), and the solution of games with both lexicographic mean-payoff and parity objectives (for liveness requirements). We present algorithms for solving both kinds of novel graph games.

References

[1]

Alpern, B., Schneider, F.B.: Defining liveness. Information Processing Letters (1985).

[2]

Alur, R., Degorre, A., Maler, O., Weiss, G.: On omega-languages defined by mean-payoff conditions. In: de Alfaro, L. (ed.) FOSSACS 2009. LNCS, vol. 5504, pp. 333-347. Springer, Heidelberg (2009).

[3]

Björklund, H., Sandberg, S., Vorobyov, S.: Memoryless determinacy of parity and mean payoff games: a simple proof. Theor. Comput. Sci. (2004).

[4]

Bloem, R., Chatterjee, K., Henzinger, T.A., Jobstmannn, B.: Better quality in synthesis through quantitative objectives. CoRR, abs/0904.2638 (2009).

[5]

Chakrabarti, A., Chatterjee, K., Henzinger, T.A., Kupferman, O., Majumdar, R.: Verifying quantitative properties using bound functions. In: Borrione, D., Paul, W. (eds.) CHARME 2005. LNCS, vol. 3725, pp. 50-64. Springer, Heidelberg (2005).

[6]

Chakrabarti, A., de Alfaro, L., Henzinger, T.A., Stoelinga, M.: Resource interfaces. In: Alur, R., Lee, I. (eds.) EMSOFT 2003. LNCS, vol. 2855, pp. 117-133. Springer, Heidelberg (2003).

[7]

Chatterjee, K., de Alfaro, L., Faella, M., Henzinger, T.A., Majumdar, R., Stoelinga, M.: Compositional quantitative reasoning. In: QEST, pp. 179-188. IEEE Computer Society Press, Los Alamitos (2006).

[8]

Chatterjee, K., Doyen, L., Henzinger, T.A.: Quantitative languages. In: Kaminski, M., Martini, S. (eds.) CSL 2008. LNCS, vol. 5213, pp. 385-400. Springer, Heidelberg (2008).

[9]

Chatterjee, K., Henzinger, T.A., Jurdzinski, M.: Mean-payoff parity games. In: Annual Symposium on Logic in Computer Science (LICS) (2005).

[10]

Chatterjee, K., Henzinger, T.A., Jurdzinski, M.: Games with secure equilibria. In: LICS 2004, pp. 160-169. IEEE, Los Alamitos (2004).

[11]

de Alfaro, L.: How to specify and verify the long-run average behavior of probabilistic systems. In: LICS 1998, pp. 454-465. IEEE Computer Society Press, Los Alamitos (1998).

[12]

de Alfaro, L., Henzinger, T.A., Majumdar, R.: Discounting the future in systems theory. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J.,Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719. Springer, Heidelberg (2003).

[13]

de Alfaro, L., Majumdar, R., Raman, V., Stoelinga, M.: Game relations and metrics. In: LICS, pp. 99-108. IEEE Computer Society Press, Los Alamitos (2007).

[14]

Desharnais, J., Gupta, V., Jagadeesan, R., Panangaden, P.: Metrics for labelled Markov systems. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 258-273. Springer, Heidelberg (1999).

[15]

Droste, M., Gastin, P.: Weighted automata and weighted logics. Theoretical Computer Science 380, 69-86 (2007).

[16]

Droste, M., Kuich,W., Rahonis, G.: Multi-valued MSO logics over words and trees. Fundamenta Informaticae 84, 305-327 (2008).

[17]

Ehrenfeucht, A., Mycielski, J.: Positional strategies for mean payoff games. International Journal of Game Theory (1979).

[18]

Karp, R.M.: A characterization of the minimum cycle mean of a digraph. Discrete Mathematics (1978).

[19]

King, V., Kupferman, O., Vardi, M.Y.: On the complexity of parity word automata. In: Honsell, F., Miculan, M. (eds.) FOSSACS 2001. LNCS, vol. 2030, p. 276. Springer, Heidelberg (2001).

[20]

Kupferman, O., Lustig, Y.: Lattice automata. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 199-213. Springer, Heidelberg (2007).

[21]

Zwick, U., Paterson, M.: The complexity of mean payoff games on graphs. Theoretical Computer Science (1996).

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Chatterjee KKatoen JMohr SWeininger MWinkler T(2024)Stochastic games with lexicographic objectivesFormal Methods in System Design10.1007/s10703-023-00411-463:1-3(40-80)Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1007/s10703-023-00411-4
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Published In

cover image Guide Proceedings

CAV '09: Proceedings of the 21st International Conference on Computer Aided Verification

June 2009

720 pages

ISBN:9783642026577

Editors:
Ahmed Bouajjani
LIAFA, University Paris Diderot (Paris 7), Case 7014, Paris Cedex 13, France 75205
,
Oded Maler
Verimag, Centre Equation, Gières, France 38610

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 23 June 2009

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Cited By

Chatterjee KKatoen JMohr SWeininger MWinkler T(2024)Stochastic games with lexicographic objectivesFormal Methods in System Design10.1007/s10703-023-00411-463:1-3(40-80)Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1007/s10703-023-00411-4
Hyland DGutierrez JWooldridge MElkind E(2023)Principal-agent Boolean gamesProceedings of the Thirty-Second International Joint Conference on Artificial Intelligence10.24963/ijcai.2023/17(144-152)Online publication date: 19-Aug-2023
https://dl.acm.org/doi/10.24963/ijcai.2023/17
Hahn EPerez MSchewe SSomenzi FTrivedi AWojtczak D(2023)Multi-objective ω-Regular Reinforcement LearningFormal Aspects of Computing10.1145/360595035:2(1-24)Online publication date: 18-Jul-2023
https://dl.acm.org/doi/10.1145/3605950
Dewes RDimitrova R(2023)Compositional High-Quality SynthesisAutomated Technology for Verification and Analysis10.1007/978-3-031-45329-8_16(334-354)Online publication date: 24-Oct-2023
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Nayak SNeider DZimmermann M(2022)Robustness-by-Construction Synthesis: Adapting to the Environment at RuntimeLeveraging Applications of Formal Methods, Verification and Validation. Verification Principles10.1007/978-3-031-19849-6_10(149-173)Online publication date: 22-Oct-2022
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Henzinger TSaraç NGorla D(2021)Quantitative and approximate monitoringProceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science10.1109/LICS52264.2021.9470547(1-14)Online publication date: 29-Jun-2021
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Cavezza DAlrajeh DGyörgy A(2021)A Weakness Measure for GR(1) FormulaeFormal Aspects of Computing10.1007/s00165-020-00519-y33:1(27-63)Online publication date: 1-Jan-2021
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Boker U(2021)Quantitative vs. Weighted AutomataReachability Problems10.1007/978-3-030-89716-1_1(3-18)Online publication date: 25-Oct-2021
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Patil MHoushmand FLesani MSen KNaik M(2020)Learning quantitative representation synthesisProceedings of the 4th ACM SIGPLAN International Workshop on Machine Learning and Programming Languages10.1145/3394450.3397467(29-37)Online publication date: 15-Jun-2020
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