Quantifier elimination for the reals with a predicate for the powers of two

Authors:
Jeremy Avigad;Yimu Yin
Affiliations:
Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA 15213, United States;Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA 15213, United States
Venue:
Theoretical Computer Science
Year:
2007

Citing 5
Cited 2

The complexity of almost linear diophantine problems

Journal of Symbolic Computation
Algorithmic algebra

Algorithmic algebra
Complexity and uniformity of elimination in Presburger arithmetic

ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
New results on quantifier elimination over real closed fields and applications to constraint databases

Journal of the ACM (JACM)
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition

Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages

A generalization of Cobham's theorem to automata over real numbers

Theoretical Computer Science
A generalization of Cobham's theorem to automata over real numbers

ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming

Quantified Score

Hi-index	5.23

Visualization

Abstract

In 1985, van den Dries showed that the theory of the reals with a predicate for the integer powers of two admits quantifier elimination in an expanded language, and is hence decidable. He gave a model-theoretical argument, which provides no apparent bounds on the complexity of a decision procedure. We provide a syntactical argument that yields a procedure that is primitive recursive, although not elementary. In particular, we show that it is possible to eliminate a single block of existential quantifiers in time 2"O"("n")^0, where n is the length of the input formula and 2"k^x denotes k-fold iterated exponentiation.