computational complexity

, Volume 7, Issue 3, pp 205-263

A quantifier elimination for the theory of p-adic numbers

  • L. EgidiAffiliated withDipartimento di Informatica, Università degli Studi di Torino, Corso Svizzera, 185, I-10149 Torino TO, Italy, e-mail:

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This paper presents a detailed analysis of a quantifier elimination algorithm for the first order theory of p-adic numbers based on a p-adic analogue of the cylindrical algebraic decomposition. It is believed that this method should lead to an elementary upper bound for the theory. The present paper gives strong arguments against this conjecture and offers a basis for further speculation.

Keywords. Complexity; theory of p-adic numbers; cylindrical algebraic decomposition.