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- W2035637454 abstract "Abstract i) We show for each context-free language L that by considering each word of L as a structure in a natural way, one turns L into a finite union of classes which satisfy a finitary analog of the characteristic properties of complete universal first order classes of structures equipped with elementary embeddings. We show this to hold for a much larger class of languages which we call free local languages, ii) We define local languages, a class of languages between free local and context-sensitive languages. Each local language L has a natural extension L ∞ to infinite words, and we prove a series of “pumping lemmas”, analogs for each local language L of the “uvxyz theorem” of context free languages: they relate the existence of large words in L or L ∞ to the existence of infinite “progressions” of words included in L , and they imply the decidability of various questions about L or L ∞ . iii) We show that the pumping lemmas of ii) are independent from strong axioms, ranging from Peano arithmetic to ZF + Mahlo cardinals. We hope that these results are useful for a model-theoretic approach to the theory of formal languages." @default.
- W2035637454 created "2016-06-24" @default.
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- W2035637454 date "1988-12-01" @default.
- W2035637454 modified "2023-09-25" @default.
- W2035637454 title "Formal languages defined by the underlying structure of their words" @default.
- W2035637454 doi "https://doi.org/10.1017/s0022481200027894" @default.
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