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We deene matchings, and show that they capture the essence of context{freeness. More precisely, we show that the class of context{ free languages coincides with the class of those sets of strings which can be deened by sentences of the form 9 b', where ' is rst order, b is a binary predicate symbol, and the range of the second order quantiier is restricted… (More)

A language L over an alphabet A is said to have a neutral letter if there is a letter e ∈ A such that inserting or deleting e's from any word in A * does not change its membership or non-membership in L. The presence of a neutral letter affects the definability of a language in first-order logic. It was conjectured that it renders all numerical predicates… (More)

BPP is the class of ail sets that can be decided by a probabilistic Turing machine with bounded error probability within a polynomial time bound. Sipser (1983) showed that BPP is contained in the polynomial hierarchy of Meyer and Stockmeyer. In this paper it is shown by pure counting arguments that BPP is contained in C!, the second level of the hierarchy.… (More)

A language L over an alphabet A is said to have a neutral letter if there is a letter e ∈ A such that inserting or deleting e's from any word in A * does not change its membership (or non–membership) in L. The presence of a neutral letter affects the definability of a language in first–order logic. It was conjectured that it renders all numerical predicates… (More)

The counting ability of weak formalisms is of interest as a measure of their expressive power. The question was investigated in several papers in complexity theory [ABO84,FKPS85,DGS86] and in weak arithmetic [PW87]. In each case, the considered formalism (AC 0 {circuits, rst{order logic, ¡0, respectively) was shown to be able to count precisely up to a… (More)