Abstract
Automatic synthesis from linear temporal logic (LTL) specifications is widely used in robotic motion planning and control of autonomous systems. A common specification pattern in such applications consists of an LTL formula describing the requirements on the behaviour of the system, together with a set of additional desirable properties. We study the synthesis problem in settings where the overall specification is unrealizable, more precisely, when some of the desirable properties have to be (temporarily) violated in order to satisfy the system’s objective. We provide a quantitative semantics of sets of safety specifications, and use it to formalize the “best-effort” satisfaction of such soft specifications while satisfying the hard LTL specification. We propose an algorithm for synthesizing implementations that are optimal with respect to this quantitative semantics. Our method builds upon the idea of bounded synthesis, and we develop a MaxSAT encoding which allows for maximizing the quantitative satisfaction of the soft specifications. We evaluate our algorithm on scenarios from robotics and power distribution networks.
R. Dimitrova—This work was done while the author was at The University of Texas at Austin.
This work was supported in part by AFRL grants UTC 17-S8401-10-C1 and FA8650-15-C-2546, and ONR grant N000141613165.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The code is available at https://github.com/MahsaGhasemi/max-realizability.
References
Almagor, S., Boker, U., Kupferman, O.: Formally reasoning about quality. J. ACM 63(3), 24:1–24:56 (2016)
Alur, R., Kanade, A., Weiss, G.: Ranking automata and games for prioritized requirements. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 240–253. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-70545-1_23
Baier, C., Katoen, J.-P.: Principles of model checking (2008)
Bloem, R., Chatterjee, K., Henzinger, T.A., Jobstmann, B.: Better quality in synthesis through quantitative objectives. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 140–156. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02658-4_14
Cimatti, A., Roveri, M., Schuppan, V., Tchaltsev, A.: Diagnostic information for realizability. In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds.) VMCAI 2008. LNCS, vol. 4905, pp. 52–67. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78163-9_9
Cimatti, A., Roveri, M., Schuppan, V., Tonetta, S.: Boolean abstraction for temporal logic satisfiability. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 532–546. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73368-3_53
Dimitrova, R., Ghasemi, M., Topcu, U.: Maximum realizability for linear temporal logic specifications. CoRR, abs/1804.00415 (2018)
Duret-Lutz, A., Lewkowicz, A., Fauchille, A., Michaud, T., Renault, E., Xu, L.: Spot 2.0 - a framework for LTL and \(\omega \) -automata manipulation. In: Proceedings of ATVA 2016. LNCS, vol. 9938 (2016)
Ehlers, R., Raman, V.: Low-effort specification debugging and analysis. In: Proceedings of SYNT 2014.EPTCS, vol. 157, pp. 117–133 (2014)
Finkbeiner, B., Schewe, S.: Bounded synthesis. STTT 15(5—-6), 519–539 (2013)
Juma, F., Hsu, E.I., McIlraith, S.A.: Preference-based planning via MaxSAT. In: Kosseim, L., Inkpen, D. (eds.) AI 2012. LNCS (LNAI), vol. 7310, pp. 109–120. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-30353-1_10
Kim, K., Fainekos, G.E., Sankaranarayanan, S.: On the minimal revision problem of specification automata. Int. J. Robot. Res. 34(12), 1515–1535 (2015)
Kupferman, O., Vardi, M.Y.: Safraless decision procedures. In: Proceedings of FOCS 2005, pp. 531–542 (2005)
Lahijanian, M., Almagor, S., Fried, D., Kavraki, L.E., Vardi, M.Y.: This time the robot settles for a cost: a quantitative approach to temporal logic planning with partial satisfaction. In: Proceedings of AAAI 2015 (2015)
Lahijanian, M., Kwiatkowska, M.Z.: Specification revision for markov decision processes with optimal trade-off. In: Proceedings of CDC 2016, pp. 7411–7418 (2016)
Martins, R., Manquinho, V., Lynce, I.: Open-WBO: a modular MaxSAT solver’. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 438–445. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_33
Schewe, S., Finkbeiner, B.: Bounded synthesis. In: Namjoshi, K.S., Yoneda, T., Higashino, T., Okamura, Y. (eds.) ATVA 2007. LNCS, vol. 4762, pp. 474–488. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75596-8_33
Tabuada, P., Neider, D.: Robust linear temporal logic. In: Proceedings of CSL 2016. LIPIcs, , vol. 62, pp. 10:1–10:21 (2016)
Tomita, T., Ueno, A., Shimakawa, M., Hagihara, S., Yonezaki, N.: Safraless LTL synthesis considering maximal realizability. Acta Inform. 54(7), 655–692 (2017)
Tumova, J., Hall, G.C., Karaman, S., Frazzoli, E., Rus, D.: Least-violating control strategy synthesis with safety rules. In: Proceedings of HSCC 2013 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Dimitrova, R., Ghasemi, M., Topcu, U. (2018). Maximum Realizability for Linear Temporal Logic Specifications. In: Lahiri, S., Wang, C. (eds) Automated Technology for Verification and Analysis. ATVA 2018. Lecture Notes in Computer Science(), vol 11138. Springer, Cham. https://doi.org/10.1007/978-3-030-01090-4_27
Download citation
DOI: https://doi.org/10.1007/978-3-030-01090-4_27
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-01089-8
Online ISBN: 978-3-030-01090-4
eBook Packages: Computer ScienceComputer Science (R0)