From Asynchronous to Synchronous Specifications for Distributed Program Synthesis

Abstract

Distributed games [7] allow expression of various distributed program synthesis problems. In such games, a team of Process players compete against a unique Environment player, each Process playing on its own arena, without explicit communications with its teammates.

The standard definition of distributed games allows some degree of asynchrony : the Environment can play only on part of the arenas, therefore concealing to some Process players that the play is going on. While this is convenient for modeling distributed problems (especially those that themselves make use of asynchrony), these games are by no means easy to manipulate, and the existing constructions are much more tedious.

In this paper, we provide a uniform reduction of any finite state distributed game, synchronous or asynchronous, to a synchronous one with the same number of players. This reduction is shown to be correct in the sense that it preserves the existence of finite state distributed winning strategies for the team of Processes. It is uniform in the sense that it is designed for arbitrary input distributed game without any prior knowledge about its satisfiability. The size of the resulting synchronous game is also linear in the size of the original asynchronous one and, moreover, there is no blowup of the size of the winning strategies. Additional expected preservation properties (e.g. information flows) are studied. Surprisingly, it seems that no such reduction exists for arbitrary (infinite state) strategies.