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Published online: 2009-03-31
The counting hierarchy in binary notationGilda Ferreira (1) Universidade Lusófona de Humanidades e Tecnologias, Lisboa, Portugal
We present a new recursion-theoretic characterization of FCH, the hierarchy of counting functions, in binary notation. Afterwards we introduce a theory of bounded arithmetic, TCA, that can be seen as a reformulation, in the binary setting, of Jan Johannsen and Chris Pollett's system D02. Using the previous inductive characterization of FCH, we show that a strategy similar to the one applied to D02 can be used in order to characterize FCH as the class of functions provably total in TCA.
Keywords: Counting hierarchy, bounded arithmetic, complexity theory
Ferreira Gilda: The counting hierarchy in binary notation. Port. Math. 66 (2009), 81-94. doi: 10.4171/PM/1832