Low-discrepancy sequence: Difference between revisions

Revision as of 01:21, 19 January 2014

A two-level grammar is a formal grammar that is used to generate another formal grammar [1], such as one with an infinite rule set [2]. This is how a Van Wijngaarden grammar was used to specify Algol68 [3]. A context free grammar that defines the rules for a second grammar can yield an effectively infinite set of rules for the derived grammar. This makes such two-level grammars more powerful than a single layer of context free grammar, because generative two-level grammars have actually been shown to be Turing complete.^[1]

Two-level grammar can also refer to a formal grammar for a two-level formal language, which is a formal language specified at two levels, for example, the levels of words and sentences.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.

Example

A well-known non-context-free language is

{a^{n} b^{n} a^{n} | n \geq 1} .

A two-level grammar for this language is the metagrammar

N ::= 1 | N1

X ::= a | b

together with grammar schema

Start ::=

⟨ a^{N} ⟩ ⟨ b^{N} ⟩ ⟨ a^{N} ⟩

⟨ X^{N 1} ⟩

::=

⟨ X^{N} ⟩ X

⟨ X^{1} ⟩

::= X

References

↑ Sintzoff, M. "Existence of van Wijngaarden syntax for every recursively enumerable set", Annales de la Société Scientifique de Bruxelles 2 (1967), 115-118.

External links

Petersson, Kent (1990), "Syntax and Semantics of Programming Languages", Draft Lecture Notes, PDF text.

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[1] Sintzoff, M. "Existence of van Wijngaarden syntax for every recursively enumerable set", Annales de la Société Scientifique de Bruxelles 2 (1967), 115-118.

[1]

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+A '''two-level grammar''' is a [[formal grammar]] that is used to generate another formal grammar [http://web.cs.wpi.edu/~jshutt/adapt/2level.html], such as one with an infinite rule set [http://www.metanotion.net/misc/thesis.pdf#search=%22van%20Wijngaarden%20grammar%20Algol68%20ACM%20Portal%22]. This is how a [[Van Wijngaarden grammar]] was used to specify Algol68 [http://burks.bton.ac.uk/burks/language/other/a68rr/rrtoc.htm]. A [[context free grammar]] that defines the rules for a second grammar can yield an effectively infinite set of rules for the derived grammar. This makes such two-level grammars more powerful than a single layer of context free grammar, because generative two-level grammars have actually been shown to be [[Turing complete]].<ref>Sintzoff, M. "Existence of van Wijngaarden syntax for every recursively enumerable set", Annales de la Société Scientifique de Bruxelles 2 (1967), 115-118.</ref>
+''Two-level grammar'' can also refer to a formal grammar for a two-level [[formal language]], which is a formal language specified at two levels, for example, the levels of words and sentences.{{Citation needed|date=February 2007}}
+==Example==
+A well-known non-context-free language is
+:<math>\{a^n b^n a^n | n \ge 1\}.</math>
+A two-level grammar for this language is the metagrammar
+:N ::= 1 | N1
+:X ::= a | b
+together with grammar schema
+:Start ::= <math> \langle a^N \rangle\langle b^N \rangle\langle a^N \rangle </math>
+:<math> \langle X^{N1} \rangle</math> ::= <math>\langle X^N \rangle X </math>
+:<math> \langle X^1 \rangle</math> ::= X
+==See also==
+*[[Affix grammar]]
+*[[Attribute grammar]]
+*[[Van Wijngaarden grammar]]
+==References==
+<references/>
+==External links==
+* Petersson, Kent (1990), "Syntax and Semantics of Programming Languages", Draft Lecture Notes, [http://www.cs.chalmers.se/~kentp/proglang.pdf PDF text].
+{{DEFAULTSORT:Two-Level Grammar}}
+[[Category:Formal languages]]
+{{compu-lang-stub}}

Low-discrepancy sequence: Difference between revisions

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