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V is a finite set; each element is called a nonterminal character or a variable. Each variable represents a different type of phrase or clause in the sentence. Variables are also sometimes called syntactic categories. Each variable defines a sub-language of the language defined by G.
The variables α and β refine the estimation of probability parameters of an PCFG. It is possible to reestimate the PCFG algorithm by finding the expected number of times a state is used in a derivation through summing all the products of α and β divided by the probability for a sequence x given the model (|).
The following grammar, with start symbol Expr, describes a simplified version of the set of all syntactical valid arithmetic expressions in programming languages like C or Algol60. Both number and variable are considered terminal symbols here for simplicity, since in a compiler front end their internal structure is usually not considered by the ...
An abstract syntax tree (AST) is a data structure used in computer science to represent the structure of a program or code snippet. It is a tree representation of the abstract syntactic structure of text (often source code) written in a formal language.
Let Σ be a finite set of distinct, unambiguous symbols (alternatively called characters), called the alphabet. A string (or word [23] or expression [24]) over Σ is any finite sequence of symbols from Σ. [25] For example, if Σ = {0, 1}, then 01011 is a string over Σ. The length of a string s is the number of symbols in s (the length of the ...
Fano's method divides the source symbols into two sets ("0" and "1") with probabilities as close to 1/2 as possible. Then those sets are themselves divided in two, and so on, until each set contains only one symbol. The codeword for that symbol is the string of "0"s and "1"s that records which half of the divides it fell on.
In computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression.The process of finding or using such a code is Huffman coding, an algorithm developed by David A. Huffman while he was a Sc.D. student at MIT, and published in the 1952 paper "A Method for the Construction of Minimum-Redundancy Codes".
The reverse construction is also possible. Given some Turing machine, it is possible to create an equivalent unrestricted grammar [1]: 222 which even uses only productions with one or more non-terminal symbols on their left-hand sides. Therefore, an arbitrary unrestricted grammar can always be equivalently converted to obey the latter form, by ...