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A straight-line grammar (sometimes abbreviated as SLG) is a formal grammar that generates exactly one string. [1] Consequently, it does not branch (every non-terminal has only one associated production rule) nor loop (if non-terminal A appears in a derivation of B, then B does not appear in a derivation of A). [1]
Straight-line grammars are widely used in the development of algorithms that execute directly on compressed structures (without prior decompression). [2] : 212
SLGs are of interest in fields like Kolmogorov complexity, Lossless data compression, Structure discovery and Compressed data structures.[ clarification needed ]
The problem of finding a context-free grammar (equivalently: an SLG) of minimal size that generates a given string is called the smallest grammar problem.[ citation needed ]
Straight-line grammars (more precisely: straight-line context-free string grammars) can be generalized to Straight-line context-free tree grammars. The latter can be used conveniently to compress trees. [2] : 212
A context-free grammar G is an SLG if:
1. for every non-terminal N, there is at most one production rule that has N as its left-hand side, and
2. the directed graph G=<V,E>, defined by V being the set of non-terminals and (A,B) ∈ E whenever B appears at the right-hand side of a production rule for A, is acyclic.
A mathematical definition of the more general formalism of straight-line context-free tree grammars can be found in Lohrey et al. [2] : 215
An SLG in Chomsky normal form is equivalent to a straight-line program.[ citation needed ]
A context-sensitive grammar (CSG) is a formal grammar in which the left-hand sides and right-hand sides of any production rules may be surrounded by a context of terminal and nonterminal symbols. Context-sensitive grammars are more general than context-free grammars, in the sense that there are languages that can be described by a CSG but not by a context-free grammar. Context-sensitive grammars are less general than unrestricted grammars. Thus, CSGs are positioned between context-free and unrestricted grammars in the Chomsky hierarchy.
In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context. In particular, in a context-free grammar, each production rule is of the form
In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information. Typically, a device that performs data compression is referred to as an encoder, and one that performs the reversal of the process (decompression) as a decoder.
In computer science, the Earley parser is an algorithm for parsing strings that belong to a given context-free language, though it may suffer problems with certain nullable grammars. The algorithm, named after its inventor, Jay Earley, is a chart parser that uses dynamic programming; it is mainly used for parsing in computational linguistics. It was first introduced in his dissertation in 1968.
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An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar. An L-system consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols, an initial "axiom" string from which to begin construction, and a mechanism for translating the generated strings into geometric structures. L-systems were introduced and developed in 1968 by Aristid Lindenmayer, a Hungarian theoretical biologist and botanist at the University of Utrecht. Lindenmayer used L-systems to describe the behaviour of plant cells and to model the growth processes of plant development. L-systems have also been used to model the morphology of a variety of organisms and can be used to generate self-similar fractals.
In computer science, the Cocke–Younger–Kasami algorithm is a parsing algorithm for context-free grammars published by Itiroo Sakai in 1961. The algorithm is named after some of its rediscoverers: John Cocke, Daniel Younger, Tadao Kasami, and Jacob T. Schwartz. It employs bottom-up parsing and dynamic programming.
Grammar theory to model symbol strings originated from work in computational linguistics aiming to understand the structure of natural languages. Probabilistic context free grammars (PCFGs) have been applied in probabilistic modeling of RNA structures almost 40 years after they were introduced in computational linguistics.
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In computer science, an ambiguous grammar is a context-free grammar for which there exists a string that can have more than one leftmost derivation or parse tree. Every non-empty context-free language admits an ambiguous grammar by introducing e.g. a duplicate rule. A language that only admits ambiguous grammars is called an inherently ambiguous language. Deterministic context-free grammars are always unambiguous, and are an important subclass of unambiguous grammars; there are non-deterministic unambiguous grammars, however.
Sequitur is a recursive algorithm developed by Craig Nevill-Manning and Ian H. Witten in 1997 that infers a hierarchical structure from a sequence of discrete symbols. The algorithm operates in linear space and time. It can be used in data compression software applications.
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Grammar-based codes or Grammar-based compression are compression algorithms based on the idea of constructing a context-free grammar (CFG) for the string to be compressed. Examples include universal lossless data compression algorithms. 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 is known to be NP-hard, so many grammar-transform algorithms are proposed from theoretical and practical viewpoints. Generally, the produced grammar is further compressed by statistical encoders like arithmetic coding.
Grammar induction is the process in machine learning of learning a formal grammar from a set of observations, thus constructing a model which accounts for the characteristics of the observed objects. More generally, grammatical inference is that branch of machine learning where the instance space consists of discrete combinatorial objects such as strings, trees and graphs.
In data compression and the theory of formal languages, the smallest grammar problem is the problem of finding the smallest context-free grammar that generates a given string of characters. The size of a grammar is defined by some authors as the number of symbols on the right side of the production rules. Others also add the number of rules to that. The problem is NP-complete. The smallest context-free grammar that generates a given string is always a straight-line grammar without useless rules.
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A formal grammar describes how to form strings from an alphabet of a formal language that 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.
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