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A $$2^{2^{2^{pn}}}$$ upper bound on the complexity of Presburger arithmetic. (English) Zbl 0381.03021

##### MSC:
 03C10 Quantifier elimination, model completeness and related topics 03D15 Complexity of computation (including implicit computational complexity) 03B25 Decidability of theories and sets of sentences
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##### References:
 [1] Borosh, I.; Treybig, L.B., Bounds on positive integral solutions of linear Diophantine equations, (), 299-304 · Zbl 0291.10014 [2] Cooper, D.C., Theorem proving in arithmetic without multiplication, Machine intelligence, 7, 91-99, (1972) · Zbl 0258.68046 [3] Ferrante, J.; Rackoff, C., A decision procedure for the first order theory of real addition with order, () · Zbl 0277.02010 [4] Fischer, M.; Rabin, M., Super-exponential complexity of Presburger arithmetic, () · Zbl 0319.68024 [5] Meyer, A., Weak monadic second order theory of successor is not elementary recursive, (1972), manuscript [6] Presburgbr, M., Über die vollstandigkeit eines gewissen systems der arithmetik ganzer zahlen, in welchen die addition als einzige operation hervortritt, Comptes-rendus du ler congres des mathématiciens des pays slavs, (1929) [7] \scM. Rabin, private communication. 1972.
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