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From asynchronous to synchronous specifications for distributed program synthesis
From asynchronous to synchronous specifications for distributed program synthesis Overview of the talk
From asynchronous to synchronous specifications for distributed - - PowerPoint PPT Presentation
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
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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)
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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)
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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)
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From asynchronous to synchronous specifications for distributed program synthesis Synchronous vs asynchronous behaviors
Distributed process
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From asynchronous to synchronous specifications for distributed program synthesis Synchronous vs asynchronous behaviors
Synchronous behaviors
Processes hand shake at every step !
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From asynchronous to synchronous specifications for distributed program synthesis Synchronous vs asynchronous behaviors
Asynchronous behaviors
Processes receive mails in mail boxes !
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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 !
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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 !
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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 !
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From asynchronous to synchronous specifications for distributed program synthesis Sequential Program synthesis
A wandering process
Goal : the process (player) needs to find his way.
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From asynchronous to synchronous specifications for distributed program synthesis Sequential Program synthesis
The wandering (simple) rules
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From asynchronous to synchronous specifications for distributed program synthesis Sequential Program synthesis
but with uncontrollable environment moves
The Wanderer against the Tour operator
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From asynchronous to synchronous specifications for distributed program synthesis Sequential Program synthesis
The wandering (real) game
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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).
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From asynchronous to synchronous specifications for distributed program synthesis Distributed Program synthesis
Synchronous scenarios
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From asynchronous to synchronous specifications for distributed program synthesis Distributed Program synthesis
Asynchronous scenarios
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From asynchronous to synchronous specifications for distributed program synthesis Distributed Program synthesis
Encoding async. into sync. (1)
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From asynchronous to synchronous specifications for distributed program synthesis Distributed Program synthesis
Encoding async. into sync. (2)
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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.
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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 !
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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.
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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 Σ1
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.
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From asynchronous to synchronous specifications for distributed program synthesis Conclusion