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IEICE Transactions on Information and Systems 2008 E91-D(4):990-995; doi:10.1093/ietisy/e91-d.4.990
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Copyright © 2008 The Institute of Electronics, Information and Communication Engineers

Regular Section -- Papers -- Computation and Computational Models

Recursion Theoretic Operators for Function Complexity Classes*

Kenya UENO1

1 The author is with the Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, 113–8656 Japan.E-mail: kenya{at}is.s.u-tokyo.ac.jp


  Abstract

We characterize the gap between time and space complexity of functions by operators and completeness. First, we introduce a new notion of operators for function complexity classes based on recursive function theory and construct an operator which generates FP SPACE from FP. Then, we introduce new function classes composed of functions whose output lengths are bounded by the input length plus some constant. We characterize FP and FP SPACE by using these classes and operators. Finally, we define a new notion of completeness for FP SPACE and show a FP SPACE-complete function.

Key Words: recursive function theory, function complexity classes, operators for complexity classes

Manuscript received August 27, 2007. Manuscript revised November 30, 2007.

* This paper was presented at The 16th Annual International Symposium on Algorithms and Computation (ISAAC 2005), Sanya, Hainan, China, December, 2005.


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