Abstract
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.
This is an outline of a projected lecture, in which I will refer extensively to and draw conclusions from results already published in [2]; and to make it as self-contained as possible, it has been necessary to quote extensively from [2], including the verbatim repetition of some of the basic definitions.
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Moschovakis, Y.N. (2005). Recursion and Complexity. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds) New Computational Paradigms. CiE 2005. Lecture Notes in Computer Science, vol 3526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494645_44
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