Prim's algorithm - Revision history

en>Runner1928: /* See also */ Added links

2014-12-12T23:28:53Z

129.21.138.98: moved to right, cleaner

2014-03-03T23:54:04Z

moved to right, cleaner

← Older revision		Revision as of 01:54, 4 March 2014
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	~~In [[computer science]] and [[formal language]] theory, a [[context-free grammar]]~~ is in '''Greibach normal form''' (GNF) if the right-hand sides of all [[production (computer science)\|production]] rules start with a [[terminal symbol]], optionally followed by some variables. A non-strict form allows one exception to this format restriction for allowing the [[empty word]] (epsilon, ε) to be a member of the described language. The normal form bears the name ~~of [[Sheila Greibach]]~~.		Alyson Meagher is the name her parents gave her but she doesn't like when people use her full title. To climb is something I truly appreciate doing. My working day occupation is a journey agent. For a while I've been in Mississippi but now I'm contemplating other choices.<br><br>My web blog: love psychics ([http://yoparo.org/content/very-best-details-about-hobbies-you-may-read yoparo.org])

	~~More precisely, a context-free grammar~~ is ~~in Greibach normal form, if all production rules are of the form:~~
	~~:<math>A \to \alpha A_1 A_2 \cdots A_n</math>~~
	or
	~~:<math>S \to \varepsilon</math>~~
	~~where <math>A</math>~~ is a ~~[[nonterminal symbol]], <math>\alpha</math> is~~ a ~~terminal symbol,~~
	~~<math>A_1 A_2 \ldots A_n</math> is a (possibly empty) sequence of nonterminal symbols not including the start symbol, ''S~~'' ~~is the start symbol, and ''ε'' is the [[empty word]].~~

	~~Observe that the grammar does not have [[left recursion]]s.~~

	~~Every context-free grammar can be transformed into an equivalent grammar in Greibach normal form~~.<~~ref~~>~~{{cite journal \| last=Greibach \| first=Sheila \| title=A New Normal-Form Theorem for Context-Free Phrase Structure Grammars \|date=January 1965\| work=Journal of the ACM \| volume=12\| issue=1}}~~<~~/ref~~> Various constructions exist. Some do not permit the second form of rule and cannot transform context-free grammars that can generate the empty word. One such construction the size of the constructed grammar is ''O(~~n<sup>4<~~/~~sup>)'' in the general case and ''O(n<sup>3<~~/~~sup>)'' if no derivation of the original grammar consists of a single nonterminal symbol, where ''n'' is the size of the original grammar~~.<ref>{{cite journal \| first1 = Norbert \| last1 = Blum \| first2 = Robert \| last2 = Koch \| title = Greibach Normal Form Transformation Revisited \| journal = Information and Computation \| volume = 150 \| issue = 1 \| year = 1999 \| pages = 112–118 \| id = {{citeseerx\|10.1.1.47.460}} }}</~~ref> This conversion can be used to prove that every [[context~~-~~free language]] can be accepted by a non~~-~~deterministic [[pushdown automaton]].~~

	~~Given a grammar in GNF and a derivable string in the grammar with length ''n'', any [[top~~-~~down parsing\|top~~-~~down parser]] will halt at depth ''n''.~~

	~~== See also ==~~
	*[[Backus-~~Naur form]]~~
	*[[Chomsky normal form]]
	*[[Kuroda normal form]]

	~~==Notes==~~
	~~<references/>~~

	~~== References ==~~
	* {{cite book \| first1 = John E. \| last1 = Hopcroft \| first2 = Jeffrey D. \| last2 = Ullman \| title = Introduction to Automata Theory, Languages and Computation \| publisher = Addison-Wesley Publishing \| location = Reading, Massachusetts \| year = 1979 \| isbn = 0-201-~~02988~~-~~X \| postscript = }} ''(See chapter 4~~.)''

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

en>JohnBlackburne: Reverted 1 edit by DarrylNester (talk): Adding links to personal site to multiple articles. (TW)

2014-01-22T00:35:44Z

Reverted 1 edit by DarrylNester (talk): Adding links to personal site to multiple articles. (TW)

← Older revision		Revision as of 02:35, 22 January 2014
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	~~Greetings~~. The ~~writer~~'~~s title~~ is ~~Phebe~~ and ~~she feels comfy when individuals use~~ the ~~full~~ title. ~~My working day occupation is a librarian. It's~~ not ~~a common thing but what she likes performing is foundation leaping~~ and ~~now she is attempting to make money with it~~. ~~South Dakota~~ is ~~exactly~~ where I'~~ve always been living~~.<br><br>~~Take~~ a ~~look~~ at ~~my website ::~~ [~~http:~~/~~/www~~.~~socialairforce~~.~~com/members/jeffekhfs/activity/13753/ www~~.~~socialairforce.com~~]		In [[computer science]] and [[formal language]] theory, a [[context-free grammar]] is in '''Greibach normal form''' (GNF) if the right-hand sides of all [[production (computer science)\|production]] rules start with a [[terminal symbol]], optionally followed by some variables. A non-strict form allows one exception to this format restriction for allowing the [[empty word]] (epsilon, ε) to be a member of the described language. The normal form bears the name of [[Sheila Greibach]].

			More precisely, a context-free grammar is in Greibach normal form, if all production rules are of the form:
			:<math>A \to \alpha A_1 A_2 \cdots A_n</math>
			or
			:<math>S \to \varepsilon</math>
			where <math>A</math> is a [[nonterminal symbol]], <math>\alpha</math> is a terminal symbol,
			<math>A_1 A_2 \ldots A_n</math> is a (possibly empty) sequence of nonterminal symbols not including the start symbol, ''S'' is the start symbol, and ''ε'' is the [[empty word]].

			Observe that the grammar does not have [[left recursion]]s.

			Every context-free grammar can be transformed into an equivalent grammar in Greibach normal form.<ref>{{cite journal \| last=Greibach \| first=Sheila \| title=A New Normal-Form Theorem for Context-Free Phrase Structure Grammars \|date=January 1965\| work=Journal of the ACM \| volume=12\| issue=1}}</ref> Various constructions exist. Some do not permit the second form of rule and cannot transform context-free grammars that can generate the empty word. One such construction the size of the constructed grammar is ''O(n<sup>4</sup>)'' in the general case and ''O(n<sup>3</sup>)'' if no derivation of the original grammar consists of a single nonterminal symbol, where ''n'' is the size of the original grammar.<ref>{{cite journal \| first1 = Norbert \| last1 = Blum \| first2 = Robert \| last2 = Koch \| title = Greibach Normal Form Transformation Revisited \| journal = Information and Computation \| volume = 150 \| issue = 1 \| year = 1999 \| pages = 112–118 \| id = {{citeseerx\|10.1.1.47.460}} }}</ref> This conversion can be used to prove that every [[context-free language]] can be accepted by a non-deterministic [[pushdown automaton]].

			Given a grammar in GNF and a derivable string in the grammar with length ''n'', any [[top-down parsing\|top-down parser]] will halt at depth ''n''.

			== See also ==
			*[[Backus-Naur form]]
			*[[Chomsky normal form]]
			*[[Kuroda normal form]]

			==Notes==
			<references/>

			== References ==
			* {{cite book \| first1 = John E. \| last1 = Hopcroft \| first2 = Jeffrey D. \| last2 = Ullman \| title = Introduction to Automata Theory, Languages and Computation \| publisher = Addison-Wesley Publishing \| location = Reading, Massachusetts \| year = 1979 \| isbn = 0-201-02988-X \| postscript = }} ''(See chapter 4.)''

			[[Category:Formal languages]]

en>David Eppstein: Kruskal and Boruvka are a little more general

2012-08-28T20:25:53Z

Kruskal and Boruvka are a little more general

New page

Greetings. The writer's title is Phebe and she feels comfy when individuals use the full title. My working day occupation is a librarian. It's not a common thing but what she likes performing is foundation leaping and now she is attempting to make money with it. South Dakota is exactly where I've always been living.<br><br>Take a look at my website :: [http://www.socialairforce.com/members/jeffekhfs/activity/13753/ www.socialairforce.com]

← Older revision		Revision as of 01:28, 13 December 2014
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	~~Alyson Meagher is the name her parents gave her but she doesn't like when people use her full title~~. ~~To climb is something~~ I ~~truly appreciate doing. My working day occupation~~ is ~~a journey agent. For a while~~ I've been ~~in Mississippi~~ but ~~now I~~'~~m contemplating other choices~~.<br><br>My ~~web~~ blog~~: love psychics (~~[http://~~yoparo~~.~~org~~/~~content~~/~~very-best-details-about-hobbies-you-may-read yoparo~~.~~org~~])		Nice to satisfy you, I am Marvella Shryock. What I adore performing is to gather badges but I've been taking on new things lately. Since she was 18 she's been working as a meter reader but she's usually wanted her own business. My family members lives in Minnesota and my family enjoys it.<br><br>My blog [http://www.videokeren.com/blog/14593 www.videokeren.com]