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Recursion theoretic operators for function complexity classes

IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 2008年第4期E91D卷 990-995页

作者： Ueno, Kenya Univ Tokyo Grad Sch Informat Sci & Technol Dept Comp Sci Tokyo 1138656 Japan

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 FPS PACE 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 FPS PACE by using these classes and operators. Finally, we define a new notion of completeness for FPS PACE and show a FPS PACE-complete function.

关键词： recursive function theory function complexity classes operators for complexity classes

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DESCRIPTIVE complexity FOR COUNTING complexity classes

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LOGICAL METHODS IN COMPUTER SCIENCE 2020年第1期16卷

作者： Arenas, Marcelo Munoz, Martin Riveros, Cristian Pontificia Univ Catolica Chile Santiago Chile IMFD Chile Santiago Chile

Descriptive complexity has been very successful in characterizing complexity classes of decision problems in terms of the properties definable in some logics. However, descriptive complexity for counting complexity classes, such as FP and #P, has not been systematically studied, and it is not as developed as its decision counterpart. In this paper, we propose a framework based on Weighted Logics to address this issue. Specifically, by focusing on the natural numbers we obtain a logic called Quantitative Second Order Logics (QSO), and show how some of its fragments can be used to capture fundamental counting complexity classes such as FP, #P and FPSPACE, among others. We also use QSO to define a hierarchy inside #P, identifying counting complexity classes with good closure and approximation properties, and which admit natural complete problems. Finally, we add recursion to QSO, and show how this extension naturally captures lower counting complexity classes such as #L

关键词： function complexity classes descriptive complexity

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