The complexity of almost linear diophantine problems
Journal of Symbolic Computation
Complexity and uniformity of elimination in Presburger arithmetic
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
On the complexity of the theories of weak direct products (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Presburger arithmetic with bounded quantifier alternation
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Decision procedures for term algebras with integer constraints
Information and Computation - Special issue: Combining logical systems
Proof Synthesis and Reflection for Linear Arithmetic
Journal of Automated Reasoning
Verifying and reflecting quantifier elimination for presburger arithmetic
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Verifying mixed real-integer quantifier elimination
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
On the satisfiability of modular arithmetic formulae
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
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We consider the first-order theory whose language has as nonlogical symbols the constant symbols 0 and 1, the binary relation symbols &equil; and This theory of integers under addition is commonly called the 'Presburger Arithmetic' and is known to be decidable for truth [Presburger (1929), Hilbert and Bernays (1968)]. We prove here that there exists a decision procedure for this theory, involving quantifier elimination, for which there is a superexponential upper bound on the size of formula produced when all variables have been eliminated.