Abstract
In system synthesis, we transform a specification into a system that is guaranteed to satisfy the specification. When the system is open, it interacts with an environment via input and output signals and its behavior depends on this interaction. An open system should satisfy its specification in all possible environments. In addition to the input signals that the system can read, an environment can also have internal signals that the system cannot read. In the above setting, of synthesis with incomplete information, we should transform a specification that refers to both readable and unreadable signals into a system whose behavior depends only on the readable signals. In this work we solve the problem of synthesis with incomplete information for specifications in μ-calculus. Since many properties of systems are naturally specified by means of fixed points, the μ-calculus is an expressive and important specification language. Our results and technique generalize and simplify previous work on synthesis. In particular, we prove that the problem of μ-calculus synthesis with incomplete information is EXPTIME-complete. Thus, it is not harder than the satisfiability or the synthesis problems for this logic.
Supported in part by NSF grant CCR-9700061, and by a grant from the Intel Corporation.
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References
G. Bhat and R. Cleaveland. Efficient local model-checking for fragments of the modal μ-calculus. In Proc. TACAS, LNCS 1055, 1996.
J.R. Burch, E.M. Clarke, K.L. McMillan, D.L. Dill, and L.J. Hwang. Symbolic model checking: 1020 states and beyond. Information & Computation, 98(2): 142–170, 1992.
M. Daniele, P. Traverso, and M.Y. Vardi. Strong cyclic planning revisited. In Proc 5th European Conference on Planning, pp. 34–46, 1999.
E.A. Emerson and E.M. Clarke. Characterizing correctness properties of parallel programs using fixpoints. In Proc. 7th ICALP, pp. 169–181, 1980.
E.A. Emerson and E.M. Clarke. Using branching time logic to synthesize synchronization skeletons. Science of Computer Programming, 2:241–266, 1982.
E.A. Emerson and J.Y. Halpern. Sometimes and not never revisited: On branching versus linear time. Journal of the ACM, 33(1):151–178, 1986.
E.A. Emerson and C. Jutla. Tree automata, Mu-calculus and determinacy. In Proc. 32nd FOCS, pp. 368–377, 1991.
E.A. Emerson, C. Jutla, and A.P. Sistla. On model-checking for fragments of μ-calculus. In Proc. 5th CAV, LNCS 697, pp. 385–396, 1993.
E.A. Emerson. Temporal and modal logic. Handbook of Theoretical Computer Science, pp. 997–1072, 1990.
M.J. Fischer and R.E. Ladner. Propositional dynamic logic of regular programs. Journal of Computer and Systems Sciences, 18:194–211, 1979.
E. Graedel and I. Walukiewicz. Guarded fixed point logic. In Proc. 14th LICS, 1999.
D. Janin and I. Walukiewicz. Automata for the modal μ-calculus and related results. In Proc. 20th MFCS, LNCS, pp. 552–562, 1995.
R. Kumar and V.K. Garg. Modeling and control of logical discrete event systems.Kluwer Academic Publishers, 1995.
D. Kozen. Results on the prepositionalμ-calculus. Theoretical Computer Science, 27:333–354, 1983.
R. Kumar and M.A. Shayman. Supervisory control of nondeterministic systems under partial observation and decentralization. SIAM J. of Control and Optimization, 1995.
O. Kupferman and M.Y. Vardi. Synthesis with incomplete informatio. In Proc. 2nd ICTL, pp. 91–106, July 1997.
O. Kupferman, M.Y. Vardi, and P. Wolper. An automata-theoretic approach to branching-time model checking. Journal of the ACM, 47(2), March 2000.
D.E. Muller and P.E. Schupp. Simulating alternating tree automata by nondeterministic automata: New results and new proofs of theorems of Rabin, McNaughton and Safra. Theoretical Computer Science, 141:69–107, 1995.
Z. Manna and R. Waldinger. A deductive approach to program synthesis. ACM TOPLAS, 2(1):90–121, 1980.
A. Pnueli and R. Rosner On the synthesis of a reactive module. In 16th POPL, 1989.
M.O. Rabin. Weakly definable relations and special automata. In Proc. Symp. Math. Logic and Foundations of Set Theory, pp. 1–23. North Holland, 1970.
R. Rosner. Modular Synthesis of Reactive Systems. PhD thesis, Weizmann Institute of Science, Rehovot, Israel, 1992.
M.Y. Vardi. An automata-theoretic approach to fair realizability and synthesis. In Proc. 7th CAV, LNCS939, pp. 267–292, 1995.
M.Y. Vardi. Reasoning about the past with two-way automata. In Proc. 25th ICALP, LNCS 1443, pp. 628–641, 1998.
T. Wilke. CTL+ is exponentially more succinct than CTL. In Proc. 19th TST & TCS, LNCS 1738, pp. 110–121, 1999.
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Kupferman, O., Vardi, M.Y. (2000). μ-Calculus Synthesis. In: Nielsen, M., Rovan, B. (eds) Mathematical Foundations of Computer Science 2000. MFCS 2000. Lecture Notes in Computer Science, vol 1893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44612-5_45
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DOI: https://doi.org/10.1007/3-540-44612-5_45
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