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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)
Building upon the known generalized-quantiier-based rst-order characterization of LOGCFL, we lay the groundwork for a deeper investigation. Speciically, we examine subclasses of LOGCFL arising from varying the arity and nesting of groupoidal quantiiers. Our work extends the elaborate theory relating monoidal quantiiers to NC 1 and its subclasses. In the(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)