Alexander Rabinovich - The Church Problem for Countable Ordinals

lmcs:1204 - Logical Methods in Computer Science, April 27, 2009, Volume 5, Issue 2 -
The Church Problem for Countable Ordinals

Authors: Alexander Rabinovich

A fundamental theorem of Buchi and Landweber shows that the Church synthesis problem is computable. Buchi and Landweber reduced the Church Problem to problems about &#969;-games and used the determinacy of such games as one of the main tools to show its computability. We consider a natural generalization of the Church problem to countable ordinals and investigate games of arbitrary countable length. We prove that determinacy and decidability parts of the Bu}chi and Landweber theorem hold for all countable ordinals and that its full extension holds for all ordinals < \omega\^\omega.

Volume: Volume 5, Issue 2
Published on: April 27, 2009
Accepted on: June 25, 2015
Submitted on: October 27, 2007
Keywords: Computer Science - Logic in Computer Science,F.4.1


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