P-m-Mitotic Sets and Arithmetical Hierarchy - Mokatsian, Arsen H.; Barseghyan, Khachatur А. (Изд-во НАН РА)
Let {0,1}∗ be the set of all finite strings of elements from {0,1}, and let P be the class of problems recognized by deterministic Turing machines, which run in polynomial time (a problem is simply a subset of {0,1}∗). This article defines the class P ( and shows that P ( is isomorphic to the class P. Based on the notions of T-mitoticity and T-autoreducibility, K.Ambos-Spies introduced the notions of P-m-mitoticity and P-m-autoreducibility. The notions of P) -m-mitoticity and P)-m-autoreducibility are introduced by analogy with the mentioned notions. The article proves that the index sets {z | W2 is P-m-mitotic} and {z | W2 is P-m-autoreducible} are Σ3-complete.
Keywords: Mathematical cybernetics; Computer science