A predicative and decidable characterization of the polynomial classes of languages

Characterizations of PTIME, PSPACE, the polynomial hierarchy and its elements are given, which are decidable (membership can be decided by syntactic inspection to the constructions), predicative (according to points of view by Leivant and others), and are obtained by means of increasing restrictions to course-of-values recursion on trees (represented in a dialect of Lisp).

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