On the Complexity of the Theories of Weak Direct Products
Name
MIT-LCS-TM-042.pdf
Size
859.69 KB
Format
Adobe PDF
Checksum (MD5)
d3fff44055ae1120966e6dc17d595862
Author(s)
Rackoff, Charles
Date Issued
January 1974
Series/Report no.
MIT-LCS-TM-042
MAC-TM-042
Abstract
Let N be the set of nonnegative integers and let < N ,+> be the weak direct product of < N,+> with itself. Mostowski[ 9 ] shows that the theory of < N ,*> is decidable, but his decision procedure isn't elementary recursive. We present here a more efficient procedure which operates within space 2 2 . As corollaries we obtain the same upper bound for the theory of finite abelian groups, the theory of finitely generated abelian groups, and the theory of the structure < N ,' > of positive ...
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