Context Free Grammars

Context-Free Grammars context-free grammatical rules —> Pj are such... 

It can be shown that the set of languages generated by context-free grammars is exactly equal to the set of languages accepted by pushdown automata [hopc79j. 

EXAMPLE Consider the following context-free grammar ... 

If L is a context-free language, there is a reverse standard form context-free grammar G = (V,E,P,S) such that L = L(G) and all rules of P are of the forms... 

FgX => uFtx => uvGtx where t is a string of basis functions and the second derivation takes at least one step, and the same test T is associated with the equations for F and G. Then test T must test tx twice and so S is not free. If we form a context-free grammar from S in the straightforward way -i.e. an equation Gx - IF Tx THEN Ex ELSE E x becomes two productions G - E... 

Let S be a monadic recursion scheme. By methods similar to the proof of Chomsky normal form for context-free grammars we can convert the equations of S to the forms ... 

The rule is parsed in a top-down fashion(l6) using a BNF driven parser according to the explicit grammar, a portion of which is shown in Figure 5. This is a fairly simple context free grammar, written in the BNF (Backus Normal Form) style.(17) A condensed version of the parse tree for the sample rule is shown in Figure 6. Semantic analysis checks for ... 

A very nice general tutorial of HMMs is given in (Rabiner, 1989). An extension of HMMs from finite automata (which is the deterministic version of a Markov chain) to context-free languages leads to the concept of a stochastic context-free grammar. Such grammars have been used in an analogous way to predict RNA secondary structures (Grate et al., 1994). 

Knudsen, B. and Hein, J. (2003) Pfold RNA secondary structure prediction using stochastic context-free grammars. Nucl. Acids Res. 31, 3423-3428. 

Mery, B., Amblard, M., Durand, L, Retore, C. A case study of the convergence of mildly context-sensitive formalisms for natural language syntax from minimalist grammars to multiple context-free grammars. INRA Rapport de recherche p. nr 6042 (2006)... 

We have defined above what we mean by structures, the ordinary line notation used by organic chemists wherein we rely on a string representation with branching indicated by parenthesization. The reader will recall that context free grammars allow more complicated nested productions, e.g. S aSb than are allowed for by regular productions. Consider grammar 3 below ... 

In Chomsky s early work [88], he proposed that the syntax of natural languages like English could be described at a basic level by a context free grammar (CFG). A CFG defines a number of rules of the form... 

Sakakibara, Y. Brown, M. Hughey, R. Mian, I.S. Sjblander, K. Underwood, R.C. Haussler, D. (1994). Stochastic context-free grammars for tRNA modeling. Nucleic Acids Res., Vol. 22, pp. 5112-5120. 

Traditional fuzzy linguistic approach The first possibility defines the linguistic term set by means of a context-free grammar, and the semantics of linguistic terms is represented by fuzzy numbers described by membership fimctions based on parameters and a semantic rule [24,59],... 

The structure of the neutral file language is formal described by a context-free grammar G(N,T,P,Z), where N denotes the set of the non-terminal characters and T the set of the terminal characters. The start character Z is defined as follows ... 

A context free grammar G is defined by the 4-Tuple (N,T,Z,R) where N denotes the non-terminal set, T denotes the terminal set, Z denotes the start character ( Z is an element of N) and R denotes the set of context free productions. The elements of R are called the R-productions of G and the union of the sets N,T is called the vocabulary V of G. 

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