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The communication hierarchy of time and space bounded parallel machines

Norbert Popély (2003)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We describe the communicating alternating machines and their simulation. We show that, in the case of communicating alternating machines which are bounded, simultaneously, by polynomial time and logarithmic space, the use of three communication levels instead of two does not increase computational power of communicating alternating machines. This resolves an open problem [2] concerning the exact position of machines with three communication levels in the hierarchy.

The Communication Hierarchy of Time and Space Bounded Parallel Machines

Norbert Popély (2010)

RAIRO - Theoretical Informatics and Applications

We describe the communicating alternating machines and their simulation. We show that, in the case of communicating alternating machines which are bounded, simultaneously, by polynomial time and logarithmic space, the use of three communication levels instead of two does not increase computational power of communicating alternating machines. This resolves an open problem [2] concerning the exact position of machines with three communication levels in the hierarchy.

The limit lemma in fragments of arithmetic

Vítězslav Švejdar (2003)

Commentationes Mathematicae Universitatis Carolinae

The recursion theoretic limit lemma, saying that each function with a 𝛴 n + 2 graph is a limit of certain function with a 𝛥 n + 1 graph, is provable in B Σ n + 1 .

Turning Borel sets into clopen sets effectively

Vassilios Gregoriades (2012)

Fundamenta Mathematicae

We present the effective version of the theorem about turning Borel sets in Polish spaces into clopen sets while preserving the Borel structure of the underlying space. We show that under some conditions the emerging parameters can be chosen in a hyperarithmetical way and using this we obtain some uniformity results.

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