en>Monkbot: /* References */Fix CS1 deprecated date parameter errors

2014-02-03T09:51:58Z

References: Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 11:51, 3 February 2014
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	~~I am 30 years old~~ and ~~my name~~ is ~~Alice Cupp~~. ~~I life~~ in ~~Concord~~ (~~United States~~).<br><br>~~Take~~ a ~~look at my website; [http~~://v7.~~wazeo~~.de/~~index~~.~~php?mod~~=~~users&action~~=~~view&id~~=~~94084 Popular mountain bike sizing~~.]		Literal movement grammars (LMGs) are a grammar formalism introduced by Groenink in 1995<ref name="groenink1995">Groenink, Annius V. 1995. Literal Movement Grammars. In ''Proceedings of the 7th EACL Conference''.</ref> intended to characterize certain extraposition phenomena of natural language such as topicalization and cross-serial dependencies. LMGs extend the class of [[Context free grammar\|CFGs]] by adding introducing pattern-matched function-like rewrite semantics, as well as the operations of variable binding and slash deletion.

			==Description==

			The basic rewrite operation of an LMG is very similar to that of a CFG, with the addition of "arguments" to the non-terminal symbols. Where a context-free rewrite rule obeys the general schema <math>S \to \alpha</math> for some non-terminal <math>S</math> and some string of terminals and/or non-terminals <math>\alpha</math>, an LMG rewrite rule obeys the general schema <math>X(x_1, ..., x_n) \to \alpha</math>, where X is a non-terminal with arity n (called a predicate in LMG terminology), and <math>\alpha</math> is a string of "items", as defined below. The arguments <math>x_i</math> are strings of terminal symbols and/or variable symbols defining an argument pattern. In the case where an argument pattern has multiple adjacent variable symbols, the argument pattern will match any and all partitions of the actual value that unify. Thus, if the predicate is <math>f(xy)</math> and the actual pattern is <math>f(ab)</math>, there are three valid matches: <math>x = \epsilon,\ y = ab;\ x = a,\ y = b;\ x = ab,\ y = \epsilon</math>. In this way, a single rule is actually a family of alternatives.

			An "item" in a literal movement grammar is one of

			* <math>f(x_1, \ldots, x_n)</math>, a predicate of arity n,
			* <math>x \text{:}f(x_1, \ldots, x_n)</math>, a variable binding x to the string produced by <math>f(x_1, ..., x_n)</math>, or
			* <math>f(x_1, \ldots, x_n)/\alpha</math>, a slash deletion of <math>f(x_1, ..., x_n)</math> by the string of terminals and/or variables <math>\alpha</math>.

			In a rule like <math>f(x_1, ..., x_m) \to \alpha\ y \text{:} g(z_1, ... z_n)\ \beta</math>, the variable y is bound to whatever terminal string the g predicate produces, and in <math>\alpha</math> and <math>\beta</math>, all occurrences of y are replaced by that string, and <math>\alpha</math> and <math>\beta</math> are produced as if terminal string had always been there.

			An item <math>x/y</math>, where x is something that produces a terminal string (either a terminal string itself or some predicate), and y is a string of terminals and/or variables, is rewritten as the empty string (<math>\epsilon</math>) if and only if <math>g(y_1, ..., y_n) = z</math>, and otherwise cannot be rewritten at all.

			==Example==

			LMGs can characterize the non-CF language <math>\{ a^n b^n c^n : n \geq 1 \}</math> as follows:

			:<math>S() \to x\text{:}A()\ B(x)</math>
			:<math>A() \to a\ A()</math>
			:<math>A() \to \epsilon</math>
			:<math>B(xy) \to a/x\ b\ B(y) c</math>
			:<math>B(\epsilon) \to \epsilon</math>

			The derivation for ''aabbcc'', using parentheses also for grouping, is therefore

			<math>S() \to x\text{:}A()\ B(x) \to x\text{:}(a\ A())\ B(x) \to x\text{:}(aa\ A())\ B(x) \to x\text{:}aa\ B(x) \to aa\ B(aa)</math>
			: <math>\to aa\ a/a\ b\ B(a)\ c \to aab\ B(a)\ c \to aab\ a/a\ b\ B()\ cc \to aabb\ B()\ cc\ \to aabbcc</math>

			==Computational Power==

			Languages generated by LMGs contain the context-free languages as a proper subset, as every CFG is an LMG where all predicates have arity 0 and no production rule contains variable bindings or slash deletions.

			==References==

			<references/>

			{{Formal languages and grammars}}

			[[Category:Formal languages]]
			[[Category:Grammar frameworks]]

en>Glrx: replace z with x

2012-07-18T20:13:05Z

replace z with x

New page

I am 30 years old and my name is Alice Cupp. I life in Concord (United States).<br><br>Take a look at my website; [http://v7.wazeo.de/index.php?mod=users&action=view&id=94084 Popular mountain bike sizing.]

Characteristic admittance - Revision history

en>Monkbot: /* References */Fix CS1 deprecated date parameter errors

en>Glrx: replace z with x