Synthesis of uninitialized systems

Thomas A. Henzinger*, Sriram C. Krishnan, Orna Kupferman, Freddy Y.C. Mang

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

8 Scopus citations


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.

Original languageAmerican English
Title of host publicationAutomata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings
EditorsPeter Widmayer, Stephan Eidenbenz, Francisco Triguero, Rafael Morales, Ricardo Conejo, Matthew Hennessy
PublisherSpringer Verlag
Number of pages13
ISBN (Print)3540438645, 9783540438649
StatePublished - 2002
Event29th International Colloquium on Automata, Languages, and Programming, ICALP 2002 - Malaga, Spain
Duration: 8 Jul 200213 Jul 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2380 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference29th International Colloquium on Automata, Languages, and Programming, ICALP 2002


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