From asynchronous to synchronous specifications for distributed - PowerPoint PPT Presentation

From asynchronous to synchronous specifications for distributed program synthesis From asynchronous to synchronous specifications for distributed program synthesis David Janin LaBRI, Bordeaux University 21st January 2008

From asynchronous to synchronous specifications for distributed program synthesis Overview of the talk Outlines Synchronous vs asynchronous behaviors Sequential Program synthesis Distributed Program synthesis More on the decidable case (hierarchical game)

From asynchronous to synchronous specifications for distributed program synthesis Overview of the talk Outlines Synchronous vs asynchronous behaviors Sequential Program synthesis Distributed Program synthesis More on the decidable case (hierarchical game)

From asynchronous to synchronous specifications for distributed program synthesis Overview of the talk Outlines Synchronous vs asynchronous behaviors Sequential Program synthesis Distributed Program synthesis More on the decidable case (hierarchical game)

From asynchronous to synchronous specifications for distributed program synthesis Overview of the talk Outlines Synchronous vs asynchronous behaviors Sequential Program synthesis Distributed Program synthesis More on the decidable case (hierarchical game)

From asynchronous to synchronous specifications for distributed program synthesis Synchronous vs asynchronous behaviors Distributed process

From asynchronous to synchronous specifications for distributed program synthesis Synchronous vs asynchronous behaviors Synchronous behaviors Processes hand shake at every step !

From asynchronous to synchronous specifications for distributed program synthesis Synchronous vs asynchronous behaviors Asynchronous behaviors Processes receive mails in mail boxes !

From asynchronous to synchronous specifications for distributed program synthesis Synchronous vs asynchronous behaviors A meta result Observation When mailboxes are of bounded size, asynchronous behaviors are (essentially) synchronous !

From asynchronous to synchronous specifications for distributed program synthesis Synchronous vs asynchronous behaviors A question Asynchronism in program synthesis In the setting of distribuetd program synthesis, can we expect a similar reduction of asynchronous problems into synchronous one ? The answer is yes as I’ll show you !

From asynchronous to synchronous specifications for distributed program synthesis Synchronous vs asynchronous behaviors A question Asynchronism in program synthesis In the setting of distribuetd program synthesis, can we expect a similar reduction of asynchronous problems into synchronous one ? The answer is yes as I’ll show you !

From asynchronous to synchronous specifications for distributed program synthesis Sequential Program synthesis A wandering process Goal : the process (player) needs to find his way.

From asynchronous to synchronous specifications for distributed program synthesis Sequential Program synthesis The wandering (simple) rules

From asynchronous to synchronous specifications for distributed program synthesis Sequential Program synthesis but with uncontrollable environment moves The Wanderer against the Tour operator

From asynchronous to synchronous specifications for distributed program synthesis Sequential Program synthesis The wandering (real) game

From asynchronous to synchronous specifications for distributed program synthesis Distributed Program synthesis n against 1 distributed game • Each process only sees his own local states. • Environment may or may not transmit (depending on his allowed moves).

From asynchronous to synchronous specifications for distributed program synthesis Distributed Program synthesis Synchronous scenarios

From asynchronous to synchronous specifications for distributed program synthesis Distributed Program synthesis Asynchronous scenarios

From asynchronous to synchronous specifications for distributed program synthesis Distributed Program synthesis Encoding async. into sync. (1)

From asynchronous to synchronous specifications for distributed program synthesis Distributed Program synthesis Encoding async. into sync. (2)

From asynchronous to synchronous specifications for distributed program synthesis Distributed Program synthesis Main results Theorem For any finite distibuted game G there is a synchronous finite distributed game H such processes do have a finite state winning distributed strategy in G if and only if they have a finite state distributed strategy in H .

From asynchronous to synchronous specifications for distributed program synthesis More on the decidable case (hierarchical game) And what about decidability issues ? The reduction from asynchronous to synchronous games may break structural decidability properties !

From asynchronous to synchronous specifications for distributed program synthesis More on the decidable case (hierarchical game) Hierarchical game • Each process sees the local states of all processes on his right.

From asynchronous to synchronous specifications for distributed program synthesis More on the decidable case (hierarchical game) Known and new results Theorem (Peterson and Reif, 80s) Finite distributed game are undecidable (even Σ 1 1 -complete) but finite distributed hierarchical games are decidable ! Theorem Reduction of distributed game to synchronous distributed game can be adapted to the hierarchical case so that decidability is preserved.

From asynchronous to synchronous specifications for distributed program synthesis Conclusion Welcome in Bordeaux from the 21st to the 23rd february