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Communication Dans Un Congrès Année : 2007

On the (high) undecidability of distributed synthesis problems

David Janin

Résumé

The distributed synthesis problem [11] is known to be undecidable. Our purpose here is to study further this undecidability. For this, we consider distributed games [8], an infinite variant of Peterson and Reif multiplayer games with partial information [10], in which Pnueli and Rosner?s distributed synthesis problem can be encoded and, when decidable [11,6,7], uniformly solved [8]. We first prove that even the simple problem of solving 2-process distributed game with reachability conditions is undecidable ( $\Sigma^0_1$ -complete). This decision problem, equivalent to two process distributed synthesis with fairly restricted FO-specification was left open [8]. We prove then that the safety case is $\Pi^0_1$ -complete. More generally, we establish a correspondence between 2-process distributed game with Mostowski?s weak parity conditions [9] and levels of the arithmetical hierarchy. finally, distributed games with general ?-regular infinitary conditions are shown to be highly undecidable ( $\Sigma^1_1$ -complete)

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Autre [cs.OH]
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Dates et versions

hal-00306387 , version 1 (25-07-2008)

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  • HAL Id : hal-00306387 , version 1

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David Janin. On the (high) undecidability of distributed synthesis problems. SOFSEM, Jan 2007, Czech Republic. pp.320--329. ⟨hal-00306387⟩

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