Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Elementary bounds for presburger arithmetic
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Positive first-order logic is NP-complete
IBM Journal of Research and Development
The finite variant property: how to get rid of some algebraic properties
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
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Let N be the set of nonnegative integers and let be the weak direct product of with itself. Mostowski[9] shows that the theory of is decidable, but his decision procedure isn't elementary recursive. We present here a more efficient procedure which operates within space [equation] 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 +,• of positive integers under multiplication. Fischer and Rabin have shown that the theory of requires time @@@@ on nondeterministic Turing machines [5]. We also obtain some very general results about the nature of the theory of the weak direct product of a structure with itself.