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)


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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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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