Portugaliae Mathematica

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Volume 66, Issue 1, 2009, pp. 81–94
DOI: 10.4171/PM/1832

The counting hierarchy in binary notation

Gilda Ferreira[1]

(1) Departamento de Matemática, Universidade Lusófona de Humanidades e Tecnologias, Av. do Campo Grande, 376, 1749-024, 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