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To compress a data sequence =, a grammar-based code transforms into a context-free grammar . The problem of finding a smallest grammar for an input sequence ( smallest grammar problem ) is known to be NP-hard, [ 2 ] so many grammar-transform algorithms are proposed from theoretical and practical viewpoints.
Context-free grammars are a special form of Semi-Thue systems that in their general form date back to the work of Axel Thue. The formalism of context-free grammars was developed in the mid-1950s by Noam Chomsky, [3] and also their classification as a special type of formal grammar (which he called phrase-structure grammars). [4]
A lookahead LR parser (LALR) generator is a software tool that reads a context-free grammar (CFG) and creates an LALR parser which is capable of parsing files written in the context-free language defined by the CFG. LALR parsers are desirable because they are very fast and small in comparison to other types of parsers.
To do so technically would require a more sophisticated grammar, like a Chomsky Type 1 grammar, also termed a context-sensitive grammar. However, parser generators for context-free grammars often support the ability for user-written code to introduce limited amounts of context-sensitivity.
The standard version of CYK operates only on context-free grammars given in Chomsky normal form (CNF). However any context-free grammar may be algorithmically transformed into a CNF grammar expressing the same language (Sipser 1997). The importance of the CYK algorithm stems from its high efficiency in certain situations.
The set of all context-free languages is identical to the set of languages accepted by pushdown automata, which makes these languages amenable to parsing.Further, for a given CFG, there is a direct way to produce a pushdown automaton for the grammar (and thereby the corresponding language), though going the other way (producing a grammar given an automaton) is not as direct.
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 can be used in data compression software applications. [2]
A weighted context-free grammar (WCFG) is a more general category of context-free grammar, where each production has a numeric weight associated with it. The weight of a specific parse tree in a WCFG is the product [7] (or sum [8]) of all rule weights in the tree. Each rule weight is included as often as the rule is used in the tree.