Lower bounds for solving linear diophantine equations on random access machines
Journal of the ACM (JACM)
Applications of Ramsey's theorem to decision tree complexity
Journal of the ACM (JACM)
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
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Tight bounds are proved for Sort, Merge, Insert, Gcd of integers, Gcd of polynomials, and Rational functions over a finite inputs domain, in a random access machine with arithmetic operations, direct and indirect addressing, unlimited power for answering YES/NO questions, branching, and tables with bounded size. These bounds are also true even if additions, subtractions, multiplications, and divisions of elements by elements of the field are not counted.In a random access machine with finitely many constants and a bounded number of types of instructions, it is proved that the complexity of a function over a countable infinite domain is equal to the complexity of the function in a sufficiently large finite subdomain.