Abstract
This paper proposes an abstraction method for compositional synthesis. Synthesis is a method to automatically compute a control program or supervisor that restricts the behaviour of a given system to ensure safety and liveness. Compositional synthesis uses repeated abstraction and simplification to combat the state-space explosion problem for large systems. The abstraction method proposed in this paper finds and removes the so-called certainly unsupervisable states. By removing these states at an early stage, the final state space can be reduced substantially. The paper describes an algorithm with cubic time complexity to compute the largest possible set of removable states. A practical example demonstrates the feasibility of the method to solve real-world problems.
Keywords
- Unsupervised Conditions
- Abstraction Method
- Supervisory Control Theory
- Uncontrollable Transitions
- Synchronous Composition
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
de Alfaro, L., Henzinger, T.A.: Interface automata. In: Proceedings of the 9th ACM SIGSOFT International Symposium on Foundations of Software Engineering 2001, pp. 109–120, Vienna, Austria (2001)
Asarin, E., Maler, O., Pnueli, A.: Symbolic controller synthesis for discrete and timed systems. In: Antsaklis, P.J., Kohn, W., Nerode, A., Sastry, S.S. (eds.) HS 1994. LNCS, vol. 999, pp. 1–20. Springer, Heidelberg (1995)
Aziz, A., Singhal, V., Swamy, G.M., Brayton, R.K.: Minimizing interacting finite state machines: a compositional approach to language containment. In: Proceedings of the IEEE International Conference on Computer Design: VLSI in Computers and Processors, ICCD ’94, pp. 255–261 (1994)
Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press, Cambridge (2008)
Baier, C., Klein, J., Klüppelholz, S.: A compositional framework for controller synthesis. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 512–527. Springer, Heidelberg (2011)
Fabian, M.: On object oriented nondeterministic supervisory control. Ph.D. thesis, Chalmers University of Technology, Göteborg, Sweden. https://publications.lib.chalmers.se/cpl/record/index.xsql?pubid=1126 (1995)
Filiot, E., Jin, N., Raskin, J.-F.: Compositional algorithms for LTL synthesis. In: Bouajjani, A., Chin, W.-N. (eds.) ATVA 2010. LNCS, vol. 6252, pp. 112–127. Springer, Heidelberg (2010)
Flordal, H., Malik, R.: Compositional verification in supervisory control. SIAM J. Control Opt. 48(3), 1914–1938 (2009)
Flordal, H., Malik, R., Fabian, M., Åkesson, K.: Compositional synthesis of maximally permissive supervisors using supervision equivalence. Discrete Event Dyn. Syst. 17(4), 475–504 (2007)
Gohari, P., Wonham, W.M.: On the complexity of supervisory control design in the RW framework. IEEE Trans. Syst. Man Cybern. 30(5), 643–652 (2000)
Hoare, C.A.R.: Communicating Sequential Processes. Prentice-Hall, Upper Saddle River (1985)
Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Boston (2001)
Lin, F., Wonham, W.M.: Decentralized control and coordination of discrete-event systems with partial observation. IEEE Trans. Autom. Control 35(12), 1330–1337 (1990)
Malik, R.: The language of certain conflicts of a nondeterministic process. Working Paper 05/2010, Dept. of Computer Science, University of Waikato, Hamilton, New Zealand. http://hdl.handle.net/10289/4108 (2010)
Malik, R., Streader, D., Reeves, S.: Conflicts and fair testing. Int. J. Found. Comput. Sci. 17(4), 797–813 (2006)
Mohajerani, S., Malik, R., Fabian, M.: A framework for compositional synthesis of modular nonblocking supervisors. IEEE Trans. Autom. Control. 59(1), 150–162 (2014)
Mooij, A.J., Stahl, C., Voorhoeve, M.: Relating fair testing and accordance for service replaceability. J. Logic Algebr. Program. 79(3–5), 233–244 (2010)
Nuutila, E.: Efficient transitive closure computation in large digraphs. Acta Polytechnica Scandinavica, Mathematics and Computing in Engineering Series, vol. 74. Finnish Academy of Technology, Helsinki (1995)
Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: Proceedings of the 16th ACM Symposium on Principles of Programming Languages, pp. 179–190 (1989)
Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pacific J. Math. 5(2), 285–309 (1955)
Wonham, W.M.: On the control of discrete-event systems. In: Nijmeijer, H., Schumacher, J.M. (eds.) Three Decades of Mathematical System Theory. LNCIS, vol. 135, pp. 542–562. Springer, Heidelberg (1989)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Ware, S., Malik, R., Mohajerani, S., Fabian, M. (2014). Certainly Unsupervisable States. In: Artho, C., Ölveczky, P. (eds) Formal Techniques for Safety-Critical Systems. FTSCS 2013. Communications in Computer and Information Science, vol 419. Springer, Cham. https://doi.org/10.1007/978-3-319-05416-2_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-05416-2_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05415-5
Online ISBN: 978-3-319-05416-2
eBook Packages: Computer ScienceComputer Science (R0)