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In classical formal language theory there is a well-known result stating equality between context-free and adult 0L languages, the first ones being generated in a sequential way whilst the second ones are generated in a parallel way. This paper generalizes the classical result and proves its validity for fuzzy context-free and newly introduced fuzzy adult 0L languages.
The class of context-free grammars is studied. We transform results reached in [10] into terminology which meets Category theory. If a context-free language L is given, our approach enables to describe lucidly the whole structure of all context-free grammars (with the same set of terminals) in Chomsky normal form generating L.
The concept of fuzzy multiset finite automata was introduced recently by Wang et al. in [14]. The idea is elaborated towards deterministic fuzzy multiset finite automata and the corresponding languages. The languages are studied with respect to some closure properties. Pumping lemmata are described for languages accepted by both non-deterministic and deterministic fuzzy multiset finite automata.
A relationship between L-order based on an L-equality and L-order based on crisp equality is explored in detail. This enables to clarify some properties of completely lattice L-ordered sets and generalize some related assertions. Namely, Bělohlávek's main theorem of fuzzy concept lattices is generalized as well as his theorem dealing with Dedekind–MacNeille completion. Analogously, completion of an...
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