Synthesis of Uninitialized Systems

  • Thomas A. Henzinger
  • Sriram C. Krishnan
  • Orna Kupferman
  • Freddy Y. C. Mang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2380)

Abstract

The sequential synthesis problem, which is closely related to Church’s solvability problem, asks, given a specification in the form of a binary relation between input and output streams, for the construction of a finite-state stream transducer that converts inputs to appropriate outputs. For efficiency reasons, practical sequential hardware is often designed to operate without prior initialization. Such hardware designs can be modeled by uninitialized state machines, which are required to satisfy their specification if started from any state. In this paper we solve the sequential synthesis problem for uninitialized systems, that is, we construct uninitialized finite-state stream transducers. We consider specifications given by LTL formulas, deterministic, nondeterministic, universal, and alternating Büchi automata. We solve this uninitialized synthesis problem by reducing it to the well-understood initialized synthesis problem. While our solution is straightforward, it leads, for some specification formalisms, to upper bounds that are exponentially worse than the complexity of the corresponding initialized problems. However, we prove lower bounds to show that our simple solutions are optimal for all considered specification formalisms. We also study the problem of deciding whether a given specification is uninitialized, that is, if its uninitialized and initialized synthesis problems coincide. We show that this problem has, for each specification formalism, the same complexity as the equivalence problem.

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References

  1. [ALW89]
    M. Abadi, L. Lamport, and P. Wolper. Realizable and unrealizable concurrent program specifications. In Proc. 16th Intl. Colloquium on Automata, Languages, and Programming, LNCS 372, pages 1–17. Springer-Verlag, 1989CrossRefGoogle Scholar
  2. [BL69]
    J.R. Büchi and L.H. Landweber. Solving sequential conditions by finitestate strategies. Transactions of the American Mathematical Society, 138:295–311, 1969.CrossRefMathSciNetGoogle Scholar
  3. [Chu62]
    A. Church. Logic, arithmetic, and automata. In Proc. Intl. Congress of Mathematicians, pages 23–35. Institut Mittag-Leffler, 1962.Google Scholar
  4. [Dil89]
    D.L. Dill. Trace Theory for Automatic Hierarchical Verification of Speed Independent Circuits. MIT Press, 1989.Google Scholar
  5. [EC82]
    E.A. Emerson and E.M. Clarke. Using branching time logic to synthesize synchronization skeletons. Science of Computer Programming, 2:241–266, 1982.MATHCrossRefGoogle Scholar
  6. [HU79]
    J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, 1987.Google Scholar
  7. [IEEE93]
    IEEE Standard 1149.1-1993. IEEE Standard Test Access Port and Bound-ary Scan Architecture. IEEE, 1993.Google Scholar
  8. [KV99]
    O. Kupferman and M.Y. Vardi. Church’s problem revisited. The Bulletin of Symbolic Logic, 5:245–263, 1999.MATHCrossRefMathSciNetGoogle Scholar
  9. [MH84]
    S. Miyano and T. Hayashi. Alternating finite automata on ω-words. Theoretical Computer Science, 32:321–230, 1984.MATHCrossRefMathSciNetGoogle Scholar
  10. [MS95]
    D.E. Muller and P.E. Schupp. Simulating aternating tree automata by nondeterministic automata: New results and new proofs of theorems of Rabin, McNaughton, and Safra. Theoretical Computer Science, 141:69–107, 1995.MATHCrossRefMathSciNetGoogle Scholar
  11. [MW80]
    Z. Manna and R. Waldinger. A deductive approach to program synthesis. ACM Transactions on Programming Languages and Systems, 2:90–121, 1980.MATHCrossRefGoogle Scholar
  12. [Pnu81]
    A. Pnueli. The temporal semantics of concurrent programs. Theoretical Computer Science, 13:45–60, 1981.MATHCrossRefMathSciNetGoogle Scholar
  13. [PR89]
    A. Pnueli and R. Rosner. On the synthesis of a reactive module. In Proc. 16th Symposium on Principles of Programming Languages, pages 179–190. ACM Press, 1989.Google Scholar
  14. [QBSP96]
    S. Qadeer, R. K. Brayton, V. Singhal, and C. Pixley. Latch redundancy removal without global reset. In Proc. Intl. Conference on Computer Design, pages 432–439. IEEE Computer Society, 1996.Google Scholar
  15. [Rab70]
    M.O. Rabin. Weakly definable relations and special automata. Mathematical Logic and Foundations of Set theory, 1970.Google Scholar
  16. [Rab72]
    M.O. Rabin. Automata on Infinite Objects and Church’s Problem. Number 13 in Regional Conference Series in Mathematics. American Mathematical Society, 1972.Google Scholar
  17. [RW89]
    P.J.G. Ramadge and W.M. Wonham. The control of discrete event systems. IEEE Transactions on Control Theory, 77:81–98, 1989.Google Scholar
  18. [Ros92]
    R. Rosner. Modular Synthesis of Reactive Systems. PhD thesis, Weizmann Institute of Science, 1992.Google Scholar
  19. [Saf88]
    S. Safra. On the complexity of omega-automata. In Proc. 29th Symposium on Foundations of Computer Science, pages 319–327. IEEE Computer Society, 1988.Google Scholar
  20. [SC85]
    A.P. Sistla and E.M. Clarke. The complexity of propositional linear temporal logic, Journal of the ACM, 32:733–749, 1985.MATHCrossRefMathSciNetGoogle Scholar
  21. [SP94]
    V. Singhal and C. Pixley. The verification problem for safe replaceability. In Proc. Conference on Computer-Aided Verification, LNCS 818, pages 311–323. Springer-Verlag, 1994.Google Scholar
  22. [VW94]
    M.Y. Vardi and P. Wolper. Reasoning about infinite computations. Information and Computation, 115:1–37, 1994.MATHCrossRefMathSciNetGoogle Scholar
  23. [Wol82]
    P. Wolper. Synthesis of Communicating Processes from Temporal Logic Specifications. PhD thesis, Stanford University, 1982.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Thomas A. Henzinger
    • 1
  • Sriram C. Krishnan
    • 2
  • Orna Kupferman
    • 3
  • Freddy Y. C. Mang
    • 4
  1. 1.Electrical Engineering and Computer SciencesUniversity of California at BerkeleyUSA
  2. 2.Cisco Systems, Inc.USA
  3. 3.School of Computer Science and EngineeringHebrew UniversityIsrael
  4. 4.Advanced Technology Group, Synopsys, Inc.USA

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