en>Carriearchdale: /* Properties */clean up, typo(s) fixed: identicaly → identically using AWB

2014-06-06T07:01:22Z

Properties: clean up, typo(s) fixed: identicaly → identically using AWB

en>BG19bot: WP:CHECKWIKI error fix for #98. Broken sub tag. Do general fixes if a problem exists. -, replaced: _{''r'' → _''r'' using AWB (9957)}

2014-03-01T09:16:06Z

WP:CHECKWIKI error fix for #98. Broken sub tag. Do general fixes if a problem exists. -, replaced: <sub>''r''</sup> → <sub>''r''</sub> using AWB (9957)

← Older revision		Revision as of 11:16, 1 March 2014
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	~~'''Boolean grammars''' are a class~~ of ~~formal grammars studied~~ in ~~[[formal language]] theory. They extend the basic type of grammars,~~ the [[context-free grammars]], with [[Logical_conjunction\|conjunction]] and [[negation]] operations. Besides these explicit operations, Boolean grammars allow implicit [[Logical_disjunction\|disjunction]] represented by multiple rules for ~~a single nonterminal symbol, which~~ is ~~the only logical connective expressible in context-free grammars. Conjunction and negation can be used, in particular,~~ to ~~specify intersection and complement of languages. An intermediate class of grammars known as [[conjunctive grammar]]s allows conjunction and disjunction,~~ but ~~not negation~~.		Emilia Shryock is my title but you can contact me anything you like. One of the very very best things in the globe for him is to collect badges but he is having difficulties to discover time for it. Hiring is his profession. Puerto Rico is where he's been residing for years and he will by no means transfer.<br><br>My blog [http://computerrepairredlands.com/solid-advice-terms-candida-albicans/ at home std testing]

	~~The rules of a Boolean grammar are of the form~~

	~~<math>A \to \alpha_1 \And \ldots \And \alpha_m \And~~
	~~\lnot\beta_1 \And \ldots \And \lnot\beta_n </math>~~

	~~where <math>A</math>~~ is ~~a nonterminal, <math>m+n \ge 1</math> and <math>\alpha_1</math>,~~ .~~.., <math>\alpha_m</math>, <math>\beta_1</math>, ..., <math>\beta_n</math> are strings formed of symbols in <math>\Sigma</math>~~ and ~~<math>N</math>~~. ~~Informally, such a rule asserts that every string~~ <~~math~~>w<~~/math~~> ~~over <math>\Sigma<~~/~~math> that satisfies each of the syntactical conditions represented by <math>\alpha_1<~~/~~math>, ..~~.~~, <math>\alpha_m<~~/~~math> and none of the syntactical conditions represented by <math>\beta_1</math>, ..., <math>\beta_n</math> therefore satisfies the condition defined by <math>A</math>.~~

	There exist several formal definitions of the language generated by a Boolean grammar. They have one thing in common: if the grammar is represented as a system of [[language equation]]s with union, intersection, complementation and concatenation, the languages generated by the grammar must be the solution of this system. The semantics differ in details, some define the languages using language equations, some draw upon ideas from the field of [[logic programming]]. However, these nontrivial issues of formal definition are mostly irrelevant for practical considerations, and one can construct grammars according to the given informal semantics. The practical properties of the model are similar to those of [[conjunctive grammar]]s, while the descriptional capabilities are further improved. In particular, some practically useful properties inherited from [[context-~~free grammars]], such as efficient parsing algorithms, are retained, see {{harvtxt\|Okhotin\|2010}}.~~

	~~==References==~~
	* {{cite journal\|title=Boolean Grammars\|journal=Information and Computation\|date=2004-10-~~10\|first=Alexander\|last=Okhotin\|coauthors=\|volume=194\|issue=1\|pages=19–48\|doi= 10.1016/j.ic.2004.03.006\|url=\|format=\|accessdate= }}~~
	* {{cite techreport\|first=Alexander\|last=Okhotin\|title=Nine Open Problems on Conjunctive and Boolean Grammars\|number=794 \|institution=TUCS\|year=2006}}
	* {{cite journal\|title=Well-founded semantics for Boolean grammars\|journal=Information and Computation\|date=2009\|first=Vassilis\|last=Kountouriotis\|coauthors=Nomikos, Christos; Rondogiannis, Panos\|volume=207\|issue=9\|pages=945–967\|doi=10.1016/~~j.ic.2009.05.002}}~~
	* Okhotin, Alexander (2010). "Fast parsing for Boolean grammars: a generalization of Valiant's algorithm", [[International Conference on Developments in Language Theory]] ~~(DLT 2010), [[Lecture Notes in Computer Science]] 6224, pp. 340-351. [http://users.utu.fi/aleokh/papers/boolean_matrix.pdf Preprint] available online.~~

	~~==See also==~~
	* [[Language equation]]s

	~~==External links==~~
	* [http://users.utu.fi/aleokh/boolean/ Okhotin's page on Boolean grammars]

	~~[[Category:Formal languages]]~~

	~~{{Formalmethods-stub}}~~

en>Pym1507: /* Formal definition */

2014-01-28T15:02:35Z

Formal definition

Show changes

en>777sms at 03:37, 14 April 2012

2012-04-14T03:37:53Z

Show changes

Subharmonic function - Revision history

en>Carriearchdale: /* Properties */clean up, typo(s) fixed: identicaly → identically using AWB

en>BG19bot: WP:CHECKWIKI error fix for #98. Broken sub tag. Do general fixes if a problem exists. -, replaced: ''r'' → ''r'' using AWB (9957)

en>Pym1507: /* Formal definition */

en>777sms at 03:37, 14 April 2012

en>BG19bot: WP:CHECKWIKI error fix for #98. Broken sub tag. Do general fixes if a problem exists. -, replaced: _{''r'' → _''r'' using AWB (9957)}