The Crane Beach Conjecture
نویسندگان
چکیده
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 inA 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 apart from the order predicate useless, i.e., that if a language L with a neutral letter is not definable in first–order logic with linear order, then it is not definable in first–order logic with any set N of numerical
منابع مشابه
An Algebraic Point of View on the Crane-Beach Conjecture
A letter e ∈ Σ is said to be neutral for a language L if it can be inserted and deleted at will in a word without affecting membership in L. The Crane-Beach Conjecture, which was recently disproved, stated that any language containing a neutral letter and definable in FO is in fact FO[<] definable and is thus a regular, star-free language. More generally, we say that a logic or a computational ...
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