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In Linear Unit Grammar (2006), the authors describe their "study of language in use and how people manage it, handle it, cope with it and interpret it". [3] It is a "descriptive apparatus and method which aims at integrating all or most of the superficially different varieties of English."
A constant function is also considered linear in this context, as it is a polynomial of degree zero or is the zero polynomial. Its graph, when there is only one variable, is a horizontal line. In this context, a function that is also a linear map (the other meaning) may be referred to as a homogeneous linear function or a linear form.
A regular grammar is a grammar that is left-linear or right-linear. Observe that by inserting new nonterminals, any linear grammar can be replaced by an equivalent one where some of the rules are left-linear and some are right-linear. For instance, the rules of G above can be replaced with S → aA A → Sb S → ε
A multilinear map of one variable is a linear map, and of two variables is a bilinear map. More generally, for any nonnegative integer , a multilinear map of k variables is called a k-linear map. If the codomain of a multilinear map is the field of scalars, it is called a multilinear form.
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 right-regular grammar (also called right-linear grammar) is a formal grammar (N, Σ, P, S) in which all production rules in P are of one of the following forms: A → a; A → aB; A → ε; where A, B, S ∈ N are non-terminal symbols, a ∈ Σ is a terminal symbol, and ε denotes the empty string, i.e. the string of length 0. S is called the ...
is the linear combination of vectors and such that = +. In mathematics, a linear combination or superposition is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
The language { www : w ∈ {a,b} *} is generable by an indexed grammar, but not by a linear indexed grammar, while both { ww : w ∈ {a,b} *} and { a n b n c n : n ≥ 1 } are generable by a linear indexed grammar. If both the original and the modified production rules are admitted, the language class remains the indexed languages. [16]
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