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Implicit recursion-theoretic characterizations of counting classes.
- Source :
-
Archive for Mathematical Logic . Nov2022, Vol. 61 Issue 7/8, p1129-1144. 16p. - Publication Year :
- 2022
-
Abstract
- We give recursion-theoretic characterizations of the counting class # P , the class of those functions which count the number of accepting computations of non-deterministic Turing machines working in polynomial time. Moreover, we characterize in a recursion-theoretic manner all the levels { # P k } k ∈ N of the counting hierarchy of functions FCH , which result from allowing queries to functions of the previous level, and FCH itself as a whole. This is done in the style of Bellantoni and Cook's safe recursion, and it places # P in the context of implicit computational complexity. Namely, it relates # P with the implicit characterizations of FPTIME (Bellantoni and Cook, Comput Complex 2:97–110, 1992) and FPSPACE (Oitavem, Math Log Q 54(3):317–323, 2008), by exploiting the features of the tree-recursion scheme of FPSPACE . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09335846
- Volume :
- 61
- Issue :
- 7/8
- Database :
- Academic Search Index
- Journal :
- Archive for Mathematical Logic
- Publication Type :
- Academic Journal
- Accession number :
- 159600703
- Full Text :
- https://doi.org/10.1007/s00153-022-00828-4