Applications of Ramsey's theorem to decision tree complexity
Journal of the ACM (JACM)
On the limits of computations with the floor function
Information and Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Lower Bounds for Computations with the Floor Operation
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
On the Power of Random Access Machines
Proceedings of the 6th Colloquium, on Automata, Languages and Programming
A characterization of the class of functions computable in polynomial time on Random Access Machines
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
On Polynomial Representations of Boolean Functions Related to Some Number Theoretic Problems
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
On the Optimality of the Binary Algorithm for the Jacobi Symbol
Fundamenta Informaticae
ACM Transactions on Computational Logic (TOCL)
Lower bounds for decision problems in imaginary, norm-Euclidean quadratic integer rings
Journal of Symbolic Computation
On the Optimality of the Binary Algorithm for the Jacobi Symbol
Fundamenta Informaticae
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It is proved that no finite computation tree with operations { +, -, *, /, mod, a and b is one, for all pairs of integers a and b. This settles a problem posed by Gro¨tschel et al. Moreover, if the constants explicitly involved in any operation performed in the tree are restricted to be “0” and “1” (and any other constant must be computed), then we prove an &OHgr;(log log n) lower bound on the depth of any computation tree with operations { +, -, *, /, mod, a and b is one, for all pairs of n-bit integers a and b.A novel technique for handling the truncation operation is implicit in the proof of this lower bound. In a companion paper, other lower bounds for a large class of problems are proved using a similar technique.