COMPUTATIONALLY COMPLEX AND PSEUDO-RANDOM ZERO-ONE VALUED FUNCTIONS††Portions of this work were carried out at Carngie-Mellon University, while the authors were in the Department of Computer Science. Portions of these results were reported in preliminary form in [1].

Publisher Summary This chapter discusses computationally complex and pseudo-random zero-one valued functions. All currently known existence proofs about large lower bounds on the computation of zero-one valued functions are based on diagonal arguments. Any intuitively simple description of a function implies a simple computation procedure for the function. A specious argument for the existence of arbitrarily complex zero-one valued functions illustrates some of the difficulties involved in finding computationally complex functions without diagonal constructions. The chapter describes the construction of zero-one valued functions, which are hard to compute and whose complexity can be precisely characterized in terms of the amount of storage space required to compute them. Any zero-one valued function can be computed quickly without auxiliary storage.

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