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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)
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)
Although in many ways, hyperedge replacement graph grammars (HRGs) are, among all graph generating mechanisms, what context-free Chomsky grammars are in the realm of string rewriting, their parsing problem is known to be, in general, NP-complete. In this paper, the main difficulty in HRG parsing is analysed and some conditions on either grammar or input(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)