Abstract
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 bruteforce search. In particular, the synthesis problem for bounded systems and environment is Sigma^P_2complete (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 complexitytheoretic point of view.
BibTeX  Entry
@InProceedings{kupferman_et_al:LIPIcs:2011:3048,
author = {Orna Kupferman and Yoad Lustig and Moshe Y. Vardi and Mihalis Yannakakis},
title = {{Temporal Synthesis for Bounded Systems and Environments}},
booktitle = {28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011) },
pages = {615626},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783939897255},
ISSN = {18688969},
year = {2011},
volume = {9},
editor = {Thomas Schwentick and Christoph D{\"u}rr},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2011/3048},
URN = {urn:nbn:de:0030drops30481},
doi = {http://dx.doi.org/10.4230/LIPIcs.STACS.2011.615},
annote = {Keywords: temporal synthesis}
}
Keywords: 

temporal synthesis 
Seminar: 

28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011) 
Issue Date: 

2011 
Date of publication: 

11.03.2011 