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For an arbitrary finite algebra (A, f(·, ·), 0, 1) one defines a double sequence a(i, j) by a(i, 0) = a(0, j) = 1 and a(i, j) = f(a(i, j − 1), a(i − 1, j)). The problem if such recurrent double sequences are ultimately zero is undecidable, even if we restrict it to the class of commutative finite algebras. A.M.S.-Classification: 03D10.
General connections between quantifier elimination and decidability for first order theories are studied and exemplified. A.M.S.-Classification: 03C10, 03D80.
Simple observations on diophantine definability over finite commutative rings lead to a characterization of those rings in terms of their diophantine behavior. A.M.S. Classification: 13M10, 11T06, 03G99.
We show that non-deterministic machines in the sense of [BSS] defined over wide classes of real analytic structures are more powerful than the corresponding deterministic machines.
We prove that all infinite Boolean rings (algebras) have the property P 6= NP according to the digital (binary) nondeterminism. A.M.S. Classification: 06E99, 03B70.
The author used the automatic proof procedure introduced in  and verified that the 4096 homomorphic recurrent double sequences with constant borders defined over Klein’s Vierergruppe K and the 4096 linear recurrent double sequences with constant border defined over the matrix ring M2(F2) can be also produced by systems of substitutions with finitely… (More)
A problem naturally arizing in the unit-cost complexity class NP over the field of complex numbers consists in deciding if an input of length 2n belongs to a special absolutely irreducible hypersurface of the affine space 2n . Consequently, the decision problem is substituted by a computation problem.