Abstract
We study the problems of synthesizing open systems as well as controllers for them. The key aspect of our model is that it caters to reactive environments, which can disable different sets of responses when reacting with the system. We deal with specifications given as formulas in CTL* and its sub-logic CTL. We show that both these problems, with specifications in CTL (CTL*), are 2EXPTIME-complete (resp. 3EXPTIME-complete). Thus, in a sense, reactive environments constitute a provably harder setting for the synthesis of open systems and controllers for them.
For a full version of this extended abstract, see Technical Report TCS-2000-03, Chennai Mathematical Institute, available at www.smi.ernet.in
On leave visiting Informatik VII, RWTH-Aachen, Germany
Supported in part by NSF grant CCR-9700061, and by a grant from the Intel Corporation.
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
Preview
Unable to display preview. Download preview PDF.
References
M. Abadi, L. Lamport, and P. Wolper. Realizable and unrealizable concurrent program specifications. In Proc. 16th ICALP, LNCS 372, 1989.
M. Antoniotti. Synthesis and verification of discrete controllers for robotics and manufacturing devices with temporal logic and the Control-D system. PhD thesis, New York University, New York, 1995.
J. R. Büchi and L.HG. Landweber. Solving sequential conditions by finite-state strategies. Trans. AMS, 138:295–311, 1969.
A. Church. Logic, arithmetics, and automata. In Proc. International Congress of Mathematicians, 1962, pages 23–35. institut Mittag-Leffler, 1963.
A. K. Chandra, D. C. Kozen, and L. J. Stockmeyer. Alternation. Journal of the Association for Computing Machinery, 28(1):114–133, January 1981.
M. Daniele, P. Traverso, and M. Y. Vardi. Strong cyclic planning revisited. In 5th European Conference on Planning, pages 34–46, 1999.
E. A. Emerson and C. Jutla. The complexity of tree automata and logics of programs. In Proc. 29th FOCS, pages 328–337, White Plains, October 1988.
E. A. Emerson. Temporal and modal logic. Handbook of Theoretical Computer Science, pages 997–1072, 1990.
D. Harel and A. Pnueli. On the development of reactive systems. In Logics and Models of Concurrent Systems, volume F-13 of NATO Advanced Summer Institutes, pages 477–498. Springer-Verlag, 1985.
R. Kumar and V. K. Garg. Modeling and control of logical discrete event systems. Kluwer Academic Publishers, 1995.
R. Kumar and M. A. Shayman. Supervisory control of nondeterministic systems under partial observation and decentralization. SIAM Journal of Control and Optimization, 1995.
O. Kupferman and M. Y. Vardi. Module checking. In Proc. 8th CAV, LNCS 1102, pages 75–86, 1996.
O. Kupferman and M. Y. Vardi. Module checking revisited. In Proc. 9th CAV, LNCS 1254, pages 36–47, 1997.
O. Kupferman and M. Y. Vardi. Church’s problem revisited. The Bulletin of Symbolic Logic, 5(2):245–263, June 1999.
O. Kupferman and M. Y. Vardi. Robust satisfaction. In Proc. 10th CONCUR, LNCS 1664, pages 383–398, 1999.
O. Kupferman and M. Y. Vardi. μ-calculus synthesis. In Proc. 25th MFCS.
L. Lamport. Sometimes is sometimes “not never”-on the temporal logic of programs. In Proc. 7th POPL pages 174–185, January 1980.
P. Madhusudan and P. S. Thiagarajan. Controllers for discrete event systems via morphisms. In Proc 9th CONCUR, LNCS 146, pages 18–33, 1998.
P. Madhusudan and P. S. Thiagarajan. Branching time controllers for discrete event systems. To appear in CONCUR’ 98 Special Issue, Theoretical Computer Science, 2000.
A. Pnueli and R. Rosner. On the synthesis of a reactive module. In Proc. 16th POPL, pages 179–190, 1989.
M. O. Rabin. Decidability of second order theories and automata on infinite trees. Transaction of the AMS, 141:1–35, 1969.
M. O. Rabin. Automata on infinite objects and Church’s problem. Amer. Mathematical Society, 1972.
S. Safra. On the complexity of ω-automata. In Proc. 29th IEEE Symposium on Foundations of Computer Science, pages 319–327, October 1988.
A. P. Sistla, M. Y. Vardi, and P. Wolper. The complementation problem for Büchi automata with applications to temporal logic. Theoretical Computer Science, 49:217–237, 1987.
W. Thomas. Languages, automata, and logic. Handbook of Formal Language Theory, III:389–455, 1997.
M. Y. Vardi. An automata-theoretic approach to fair realizability and synthesis. In Proc. 7th CAV, LNCS 939, pages 267–292, 1995.
M. Y. Vardi and L. Stockmeyer. Improved upper and lower bounds for modal logics of programs. In Proc 17th STOC, pages 240–251, 1985.
M. Y. Vardi and P. Wolper. Automata-theoretic techniques for modal logics of programs. Journal of Computer and System Science, 32(2):182–221, 1986.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kupferman, O., Madhusudan, P., Thiagarajan, P.S., Vardi, M.Y. (2000). Open Systems in Reactive Environments: Control and Synthesis. In: Palamidessi, C. (eds) CONCUR 2000 — Concurrency Theory. CONCUR 2000. Lecture Notes in Computer Science, vol 1877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44618-4_9
Download citation
DOI: https://doi.org/10.1007/3-540-44618-4_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67897-7
Online ISBN: 978-3-540-44618-7
eBook Packages: Springer Book Archive