The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
On the Optimality of the Binary Algorithm for the Jacobi Symbol
Fundamenta Informaticae
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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My purpose in this lecture is to explain how the representation of algorithms by recursive programs can be used in complexity theory, especially in the derivation of lower bounds for worst-case time complexity, which apply to all—or, at least, a very large class of—algorithms. It may be argued that recursive programs are not a new computational paradigm, since their manifestation as Herbrand-Gödel-Kleene systems was present at the very beginning of the modern theory of computability, in 1934. But they have been dissed as tools for complexity analysis, and part of my mission here is to rehabilitate them.