Temporal synthesis for bounded systems and environments

Orna Kupferman, Yoad Lustig, Moshe Y. Vardi, Mihalis Yannakakis

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


Temporal synthesis is the automated construction of a system from its temporal specification. It is by now realized that requiring the synthesized system to satisfy the specifications against all possible environments may be too demanding, and, dually, allowing all systems may be not demanding enough. In this work we study bounded temporal synthesis, in which bounds on the sizes of the state space of the system and the environment are additional parameters to the synthesis problem. This study is motivated by the fact that such bounds may indeed change the answer to the synthesis problem, as well as the theoretical and computational aspects of the synthesis problem. In particular, a finer analysis of synthesis, which takes system and environment sizes into account, yields deeper insight into the quantificational structure of the synthesis problem and the relationship between strong synthesis - there exists a system such that for all environments, the specification holds, and weak synthesis - for all environments there exists a system such that the specification holds. We first show that unlike the unbounded setting, where determinacy of regular games implies that strong and weak synthesis coincide, these notions do not coincide in the bounded setting. We then turn to study the complexity of deciding strong and weak synthesis. We show that bounding the size of the system or both the system and the environment, turns the synthesis problem into a search problem, and one cannot expect to do better than brute-force search. In particular, the synthesis problem for bounded systems and environment is ΣP2 -complete (in terms of the bounds, for a specification given by a deterministic automaton). We also show that while bounding the environment may lead to the synthesis of specifications that are otherwise unrealizable, such relaxation of the problem comes at a high price from a complexity-theoretic point of view.

Original languageAmerican English
Title of host publication28th International Symposium on Theoretical Aspects of Computer Science, STACS 2011
Number of pages12
StatePublished - 2011
Event28th International Symposium on Theoretical Aspects of Computer Science, STACS 2011 - Dortmund, Germany
Duration: 10 Mar 201112 Mar 2011

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs


Conference28th International Symposium on Theoretical Aspects of Computer Science, STACS 2011

All Science Journal Classification (ASJC) codes

  • Software


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