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It includes block codes, the multilevel pattern matching (MPM) algorithm, [3] variations of the incremental parsing Lempel-Ziv code, [4] and many other new universal lossless compression algorithms. Grammar-based codes are universal in the sense that they can achieve asymptotically the entropy rate of any stationary, ergodic source with a ...
Sequitur (or Nevill-Manning–Witten algorithm) is a recursive algorithm developed by Craig Nevill-Manning and Ian H. Witten in 1997 [1] that infers a hierarchical structure (context-free grammar) from a sequence of discrete symbols. The algorithm operates in linear space and time.
It is decidable whether a given grammar is a regular grammar, [f] as well as whether it is an LL grammar for a given k≥0. [26]: 233 If k is not given, the latter problem is undecidable. [26]: 252 Given a context-free grammar, it is not decidable whether its language is regular, [27] nor whether it is an LL(k) language for a given k.
To convert a grammar to Chomsky normal form, a sequence of simple transformations is applied in a certain order; this is described in most textbooks on automata theory. [4]: 87–94 [5] [6] [7] The presentation here follows Hopcroft, Ullman (1979), but is adapted to use the transformation names from Lange, Leiß (2009).
It is named after Sige-Yuki Kuroda, who originally called it a linear bounded grammar, a terminology that was also used by a few other authors thereafter. [ 3 ] Every grammar in Kuroda normal form is noncontracting , and therefore, generates a context-sensitive language .
Any context-free grammar that does not generate the empty string can be represented in CNF using only production rules of the forms and ; to allow for the empty string, one can explicitly allow , where is the start symbol.
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A formal grammar describes which strings from an alphabet of a formal language are valid according to the language's syntax. A grammar does not describe the meaning of the strings or what can be done with them in whatever context—only their form. A formal grammar is defined as a set of production rules for such strings in a formal language.