Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Compositional construction of most general controllers

  • Original Article
  • Published:
Acta Informatica Aims and scope Submit manuscript

Abstract

Given a system \({\fancyscript{A}}\) and an objective \(\varPhi \), the task of controller synthesis is to design a decision making policy that ensures \(\varPhi \) to be satisfied. This article deals with transition system-like system models and controllers that base their decisions on the observables of the actions performed so far. We present a framework for the compositional construction of controllers for conjunctive sequences of linear-time objectives in an online manner. For this approach, it is crucial that the controllers enforce the objectives in a most general manner, being as permissive as possible. We then present game-based algorithms for the construction of such most general controllers for invariance, reachability and \(\omega \)-regular objectives.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Abadi, M., Lamport, L., Wolper, P.: Realizable and unrealizable specifications of reactive systems. In: 16th Colloquium on Automata, Languages and Programming (ICALP’89), LNCS, vol. 372, pp. 1–17. Springer (1989)

  2. Arbab, F.: Reo: a channel-based coordination model for component composition. Math. Struct. Comput. Sci. 14(3), 329–366 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. Asarin, E., Bournez, O., Dang, T., Maler, O., Pnueli, A.: Effective synthesis of switching controllers for linear systems. IEEE Spec. Issue Hybrid Syst. 88, 1011–1025 (2000)

    Google Scholar 

  4. Asarin, E., Maler, O., Pnueli, A.: Symbolic controller synthesis for discrete and timed systems. In: Hybrid Systems II, LNCS, vol. 999, pp. 1–20. Springer (1995)

  5. Baier, C., Blechmann, T., Klein, J., Klüppelholz, S.: Formal verification for components and connectors. In: 7th Symposium on Formal Methods for Components and Objects (FMCO’08), LNCS, vol. 5751, pp. 82–101. Springer (2008)

  6. Baier, C., Blechmann, T., Klein, J., Klüppelholz, S.: A uniform framework for modeling and verifying components and connectors. In: 11th Conference on Coordination Models and Languages (COORD’09), LNCS, vol. 5521, pp. 247–267. Springer (2009)

  7. Baier, C., Klein, J., Klüppelholz, S.: A compositional framework for controller synthesis. In: 22nd Conference on Concurrency Theory (CONCUR’11), LNCS, vol. 6901, pp. 512–527. Springer (2011)

  8. Baier, C., Klein, J., Klüppelholz, S.: Modeling and verification of components and connectors. In: 11th International School on Formal Methods for the Design of Computer, Communication and Software Systems (SFM’11), LNCS, vol. 6659, pp. 114–147. Springer (2011)

  9. Baier, C., Klein, J., Klüppelholz, S.: Synthesis of Reo connectors for strategies and controllers. Fundam. Inform. 130(1), 1–20 (2014)

    MATH  Google Scholar 

  10. Baier, C., Sirjani, M., Arbab, F., Rutten, J.J.M.M.: Modeling component connectors in Reo by constraint automata. Sci. Comput. Program. 61(2), 75–113 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  11. Bernet, J., Janin, D., Walukiewicz, I.: Permissive strategies: from parity games to safety games. RAIRO Theor. Inf. Appl. 36(3), 261–275 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  12. Berwanger, D., Chatterjee, K., Wulf, M.D., Doyen, L., Henzinger, T.A.: Strategy construction for parity games with imperfect information. Inf. Comput. 208(10), 1206–1220 (2010)

    Article  MATH  Google Scholar 

  13. Berwanger, D., Doyen, L.: On the power of imperfect information. In: 28th Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS’08), Leibniz International Proceedings in Informatics, vol. 2, pp. 73–82. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2008)

  14. 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)

    Article  MATH  MathSciNet  Google Scholar 

  15. Bouyer, P., Duflot, M., Markey, N., Renault, G.: Measuring permissivity in finite games. In: 20th Conference on Concurrency Theory (CONCUR’09), LNCS, vol. 5710, pp. 196–210. Springer (2009)

  16. Bouyer, P., Markey, N., Olschewski, J., Ummels, M.: Measuring permissiveness in parity games: Mean-payoff parity games revisited. In: 9th Symposium on Automated Technology for Verification and Analysis (ATVA’11), LNCS, vol. 6996, pp. 135–149. Springer (2011)

  17. Büchi, J.R., Landweber, L.H.: Solving sequential conditions by finite-state strategies. Trans. Am. Math. Soc. 138, 295–311 (1969)

    Article  MATH  Google Scholar 

  18. Chatterjee, K., Doyen, L.: The complexity of partial-observation parity games. In: 17th Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR’10), LNCS, vol. 6397, pp. 1–14. Springer (2010)

  19. Chatterjee, K., Henzinger, T.A., Jobstmann, B.: Environment assumptions for synthesis. In: 19th Conference on Concurrency Theory (CONCUR’08), LNCS, vol. 5201, pp. 147–161. Springer (2008)

  20. Church, A.: Logic, arithmetic, and automata. In: Proceedings of the International Congress of Mathematicians (ICM’62), pp. 23–35. Institut Mittag-Leffler (1963)

  21. Dziembowski, S., Jurdzinski, M., Walukiewicz, I.: How much memory is needed to win infinite games? In: 12th Symposium on Logic in Computer Science (LICS’97), pp. 99–110. IEEE Computer Society Press (1997)

  22. Ehlers, R., Finkbeiner, B.: Reactive safety. In: 2nd Symposium on Games, Automata, Logics and Formal Verification (GandALF’11), EPTCS, vol. 54, pp. 178–191 (2011)

  23. Emerson, E.A., Jutla, C.S.: The complexity of tree automata and logics of programs. In: 29th Symposium on Foundations of Computer Science (FOCS’88), pp. 328–337. IEEE Computer Society Press (1988)

  24. Emerson, E.A., Jutla, C.S.: The complexity of tree automata and logics of programs. SIAM J. Comput. 29(1), 132–158 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  25. Filiot, E., Jin, N., Raskin, J.F.: Compositional algorithms for LTL synthesis. In: 8th Symposium on Automated Technology for Verification and Analysis (ATVA’10), LNCS, vol. 6252, pp. 112–127. Springer (2010)

  26. Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games: A Guide to Current Research, LNCS, vol. 2500. Springer (2002)

  27. Jobstmann, B., Bloem, R.: Optimizations for LTL synthesis. In: 6th Conference on Formal Methods in Computer-Aided Design (FMCAD’06), pp. 117–124. IEEE Computer Society Press (2006)

  28. Jobstmann, B., Galler, S.J., Weiglhofer, M., Bloem, R.: Anzu: A tool for property synthesis. In: 19th Conference on Computer Aided Verification (CAV’07), LNCS, vol. 4590, pp. 258–262. Springer (2007)

  29. Klein, J.: Compositional synthesis and most general controllers. Ph.D. thesis, Technische Universität Dresden (2013). http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-130654

  30. Kuijper, W., van de Pol, J.: Compositional control synthesis for partially observable systems. In: 20th Conference on Concurrency Theory (CONCUR’09), LNCS, vol. 5710, pp. 431–447. Springer (2009)

  31. Kuijper, W., van de Pol, J.: Computing weakest strategies for safety games of imperfect information. In: 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS’09), LNCS, vol. 5505, pp. 92–106. Springer (2009)

  32. Kupferman, O., Madhusudan, P., Thiagarajan, P.S., Vardi, M.Y.: Open systems in reactive environments: Control and synthesis. In: 11th Conference on Concurrency Theory (CONCUR’00), LNCS, vol. 1877, pp. 92–107 (2000)

  33. Kupferman, O., Piterman, N., Vardi, M.Y.: Safraless compositional synthesis. In: 18th Conference on Computer Aided Verification (CAV’06), LNCS, vol. 4144, pp. 31–44. Springer (2006)

  34. Kupferman, O., Vardi, M.Y.: Synthesis with incomplete informatio. In: 2nd International Conference on Temporal Logic (ICTL’97), pp. 91–106. Kluwer Academic Publishers (1997)

  35. Kupferman, O., Vardi, M.Y.: Synthesis of trigger properties. In: 16th Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR’10), LNCS, vol. 6355, pp. 312–331. Springer (2010)

  36. Kupferman, O., Weiner, S.: Environment-friendly safety. In: 8th Haifa Verification Conference (HVC’12), LNCS, vol. 7857, pp. 227–242. Springer (2013)

  37. Mari, F., Melatti, I., Salvo, I., Tronci, E.: Model-based synthesis of control software from system-level formal specifications. ACM Trans. Softw. Eng. Methodol. 23(1), 6 (2014)

    Article  Google Scholar 

  38. Mohalik, S., Walukiewicz, I.: Distributed games. In: 23rd Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS’03), LNCS, vol. 2914, pp. 338–351 (2003)

  39. Morgenstern, A.: Symbolic controller synthesis for LTL specifications. Ph.D. thesis, Technische Universität Kaiserslautern (2010)

  40. Morgenstern, A., Schneider, K.: Exploiting the temporal logic hierarchy and the non-confluence property for efficient LTL synthesis. In: 1st Symposium on Games, Automata, Logic, and Formal Verification (GandALF’10), Electronic Proceedings in Theoretical Computer Science, vol. 25, pp. 89–102. Elsevier (2010)

  41. Neider, D., Rabinovich, R., Zimmermann, M.: Down the borel hierarchy: Solving Muller games via safety games. In: 3rd Symposium on Games, Automata, Logics and Formal Verification (GandALF’12), Electronic Proceedings in Theoretical Computer Science, vol. 96, pp. 169–182. Elsevier (2012)

  42. Pinchinat, S., Riedweg, S.: You can always compute maximally permissive controllers under partial observation when they exist. In: 2005 American Control Conference (2005)

  43. Pnueli, A.: The temporal logic of programs. In: 18th Symposium on Foundations of Computer Science (FOCS’77), pp. 46–57. IEEE Computer Society Press (1977)

  44. Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: 16th ACM Symposium on Principles of Programming Languages (POPL’89), pp. 179–190. ACM (1989)

  45. Pnueli, A., Rosner, R.: Distributed reactive systems are hard to synthesize. In: 31st Symposium on Foundations of Computer Science (FOCS’90), Volume II, pp. 746–757. IEEE Computer Society Press (1990)

  46. Puchala, B.: Asynchronous omega-regular games with partial information. In: 35th Symposium on the Mathematical Foundations of Computer Science (MFCS’10), LNCS, vol. 6281, pp. 592–603. Springer (2010)

  47. Rabin, M.O.: Automata on Infinite Objects and Church’s Problem. American Mathematical Society (1972)

  48. Ramadge, P.J., Wonham, W.M.: Supervisory control of a class of discrete event processes. SIAM J. Control Optim. 25(1), 206–230 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  49. Raskin, J.F., Chatterjee, K., Doyen, L., Henzinger, T.A.: Algorithms for \(\omega \)-regular games with imperfect information. Log. Methods Comput. Sci. 3(3:4), 1–23 (2007)

  50. Reif, J.H.: The complexity of two-player games of incomplete information. J. Comput. Syst. Sci. 29(2), 274–301 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  51. Sohail, S., Somenzi, F.: Safety first: a two-stage algorithm for the synthesis of reactive systems. STTT 15(5–6), 433–454 (2013)

    Article  Google Scholar 

  52. Thomas, W.: Languages, automata, and logic. In: Handbook of Formal Languages, vol. III, pp. 389–455. Springer (1997)

  53. Vardi, M.Y.: An automata-theoretic approach to fair realizability and synthesis. In: 7th Conference on Computer Aided Verification (CAV’95), LNCS, vol. 939, pp. 267–278. Springer (1995)

  54. Wonham, W.M.: On the control of discrete-event systems. In: Three Decades of Mathematical System Theory, Lecture Notes in Control and Information Sciences, vol. 135, pp. 542–562. Springer (1989)

Download references

Author information

Authors and Affiliations

  1. Technische Universität Dresden, Fakultät Informatik, 01062, Dresden, Germany

    Joachim Klein, Christel Baier & Sascha Klüppelholz

Authors
  1. Joachim Klein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christel Baier
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sascha Klüppelholz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joachim Klein.

Additional information

The authors are supported by the DFG through the collaborative research centre HAEC (SFB 912), the Excellence Initiative by the German Federal and State Governments (cluster of excellence cfAED and Institutional Strategy), the Graduiertenkolleg QuantLA (1763), and the DFG/NWO-project ROCKS, and the EU-FP-7 grant MEALS (295261).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Klein, J., Baier, C. & Klüppelholz, S. Compositional construction of most general controllers. Acta Informatica 52, 443–482 (2015). https://doi.org/10.1007/s00236-015-0239-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00236-015-0239-9

Search

Navigation