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Topic: Greibach normal form

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Chomsky normal form

Kuroda normal form

Sheila Greibach

Chomsky hierarchy

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Parser

Pushdown automaton

Nondeterministic finite state machine

Abstract syntax tree

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	Sheila Greibach - Wikipedia, the free encyclopedia
		Sheila Greibach (1939-) is a researcher in formal languages, automata, compiler theory in particular; and computer science in general.
		Besides establishing the normal form (Greibach normal form) for context-free grammars now named after her, in 1965, she also investigated properties of W-grammars, pushdown automata, and decidability problems.
		The family of quasi-realtime languages forms an abstract family of languages closed under intersection, linear erasing, and reversal.
	en.wikipedia.org /wiki/Sheila_Greibach (1010 words)

	NationMaster - Encyclopedia: Chomsky hierarchy
		A context-sensitive grammar is a formal grammar G = (N, Σ, P, S) such that all rules in P are of the form αAβ → αγβ with A in N (i.
		In linguistics and computer science, a context-free grammar (CFG) is a formal grammar in which every production rule is of the form V â†’ w where V is a non-terminal symbol and w is a string consisting of terminals and/or non-terminals.
		A linear bounded automaton (plural linear bounded automata, abbreviated LBA) is a restricted form of a Turing machine.
	www.nationmaster.com /encyclopedia/Chomsky-hierarchy (1928 words)

	CMSC 451 Lecture 17, Greibach Normal Form (Site not responding. Last check: 2007-09-19)
		Greibach Normal Form of a CFG has all productions of the form A ->aV Where 'A' is a variable, 'a' is exactly one terminal and 'V' is a string of none or more variables.
		Every CFG can be rewritten in Greibach Normal Form.
		Greibach Normal Form will be used to construct a PushDown Automata that recognizes the language generated by a Context Free Grammar.
	www.cs.umbc.edu /~squire/s04-451/cs451_l17.html (139 words)

	Greibach normal form (Site not responding. Last check: 2007-09-19)
		No grammar in GNF can generate the null string.
		Conversely, every context-free grammar which does not generate the null string can be transformed into an equivalent grammar in Greibach normal form.
		Greibach normal form is named for Sheila Greibach (1939 -), who is currently Professor of Computer Science at the University of California, Los Angeles.
	www.serebella.com /encyclopedia/article-Greibach_normal_form.html (314 words)

	normalizing
		A "normal form" is a restricted form of some mathematical formalism that preserves the original meaning of the thing, and normalization is the process by which an arbitrary instance of the mathematical formalism is converted into the normal form.
		A CFG may be converted into a pushdown automaton that accepts the same language by normalizing the CFG into a suitable normal form first (Greibach normal form is traditionally used for this purpose IIRC).
		The database normal forms are in the same way restricted models of the original data.
	www.codecomments.com /message419053.html (319 words)

	[No title]
		Some normal forms We note that each of the grammars G7, G8 and G9 have a different form but generate the same language.
		The grammar G8 is in Chomsky normal form.
		The grammar G9 is in Greibach normal form.
	www.soc.napier.ac.uk /module.php3?op=getlecture&cloaking=no&lectureid=317141 (1191 words)

	Publications G. Rozenberg
		Normal forms for contextual grammars, in: Mathematical Aspects of Natural and Formal Languages (G. Paun, ed.), World Scientific Series in Computer Science, v.
		Many-to-one simulation in EOL forms is decidable, Applied Mathematics 2, 233-247 (with R. Verraedt), 1980.
		Simple EOL forms under uniform interpretation generating CF languages, LNCS 62, 1-14, Springer Verlag (with J. Albert, H. Maurer), 1978.
	www.liacs.nl /CS/TCS/pubrozenberg.html (8997 words)

	CSC 4170 Normal Forms of Context-Free Grammars (Site not responding. Last check: 2007-09-19)
		Chomsky Normal Form is particularly useful for programs that have to manipulate grammars.
		Grammars in Greibach Normal Form are typically ugly and much longer than the cfg from which they were derived.
		Greibach Normal Form is useful for proving the equivalence of cfgs and npdas.
	www.seas.upenn.edu /~cit596/notes/dave/npda-cfg2.html (126 words)

	[No title]
		This is often referred to as being "ambiguous." The restriction to Greibach Normal Form is an attempt to avoid this problem and keep the CFG unambiguous.
		It is possible to convert any CFG into one in Greibach Normal Form so this restriction is only an inconvenience.
		I think it is possible to play with the parser and use non- Greibach Normal Form CFGs, but I haven't had the time yet.
	www.nic.funet.fi /pub/crypt/old/mimic/Mimic-Manual.txt (2091 words)

	Greibach Normal Form in Algebraically Complete Semirings (Site not responding. Last check: 2007-09-19)
		We give inequational and equational axioms for semirings with a fixed-point operator and formally develop a fragment of the theory of context-free languages.
		In particular, we show that Greibach's normal form theorem depends only on a few equational properties of least pre-fixed-points in semirings, and elimination of chain- and deletion rules depend on their inequational properties (and the idempotency of addition).
		It follows that these normal form theorems also hold in non-continuous semirings having enough fixed-points
	www.brics.dk /RS/02/46/index.html (76 words)

	Notations for context-free grammars: BNF, Syntax Diagrams, EBNF
		BNF = Backus Normal Form or Backus Naur Form.
		He also points out that BNF is not a "Normal Form", which would imply there were some restrictions on how a grammar could be written down, as in e.g.
		The form of BNF used is essentially that accepted by yacc/bison.)
	www.cs.man.ac.uk /~pjj/bnf/bnf.html (1329 words)

	[No title] (Site not responding. Last check: 2007-09-19)
		Conversion from an Arbitrary CFG to Chomsky Normal Form 2.
		Conversion from Chomsky Normal Form to Greibach Normal Form 3.
		Conversion from Chomsky Normal Form to Greibach Normal Form -------------------------------------------------------------- Left Recursion -------------- A --> A u where u is a string over V (_) \Sigma ^ Direct Left Recursion * A ===> A v ^ Indirect Left Recursion Lemma ----- CFG G=(V,\Sigma,P,S) If A --> u B v and B --> w_1
	www2.ics.hawaii.edu /~sugihara/course/ics441s95/note/3-01n13 (343 words)

	[No title] (Site not responding. Last check: 2007-09-19)
		We develop a direct method for placing a given context-free grammar into Greibach normal form with only polynomial increase of its size; i.e., we don't use any algebraic concept like formal power series.
		Starting with a cfg G in Chomsky normal form, we will use standard methods for the construction of an equivalent context-free grammar from a finite automaton and vice versa for transformation of G into an equivalent cfg G 0 in Greibach normal form.
		The size of the constructed grammar is O(jGj 4) instead of O(jGj 6), which we would obtain if we transform G into Chomsky normal form and then into Greibach normal form.
	tennessee.cc.vt.edu /~akrowne/citidel/export/ri_ncstrl_dump/OAI.CITIDEL_RI.3900.txt (107 words)

	[No title] (Site not responding. Last check: 2007-09-19)
		Some example transformations on context-free grammars are Chomsky Normal Form, Greibach Normal Form, Double Greibach Normal Form, Extended Greibach Normal Form, to name a few.
		Even with the same normal form, different researchers have suggested different algorithms that have different focuses, including simplicity, efficiency, grammar size, and more.
		The purpose of this thesis is to analyze the logic behind different algorithms for Greibach Normal Form transformation, and how their performance varies.
	www.cs.ust.hk /pg/defenses/S06/edgarho-24-03-2006.txt (256 words)

	Top-down Parsing and LL(1) Languages
		We convert the grammar to Greibach normal form and jot down the one state pushdown machine that recognizes strings from the language which are generated by the grammar.
		It is of course not in the necessary form, but with the operation presented in figure 1, we can fix that.
		We can prevent this by presenting the s-grammar in Greibach normal form by turning all terminals that do not begin the right-hand side into nonterminals.
	www.cs.engr.uky.edu /~lewis/essays/compilers/ll-lang.html (1479 words)

	[No title] (Site not responding. Last check: 2007-09-19)
		CS301 LAB 1 Write a program in C++ that takes in one or more Context Free Grammars and outputs the grammars in Greibach Normal Form.
		"Ordered form" is defined to be such that the leftmost symbol on the right hand side of every rule has a Terminal or a "higher order" Nonterminal compared to the Left-Hand-Side Nonterminal.
		The third major module will be to do the final substitution that puts the grammar in Greibach Normal Form.
	www.cs.colostate.edu /~whitley/CS301/Lab (224 words)

	Transition Diagram Systems and Normal Form Algorithms (ResearchIndex) (Site not responding. Last check: 2007-09-19)
		Abstract: We investigate the complexity of a variety of normal-form transformations for transition diagram systems, which are a parsing view of extended context-free grammars.
		10 A new normal form theorem for context-free phrase structure..
		6 Extended context-free grammars and normal form transformatio..
	sherry.ifi.unizh.ch /63731.html (546 words)

	COMP360 Exam 3 study guide
		Draw a finite state automaton that recognizes decimal numbers that are evenly divisible by 5.
		What is Greibach Normal Form and why is it useful?
		All rules in Greibach Normal Form grammars start with a terminal symbol.
	williams.comp.ncat.edu /COMP360/Exam3study.htm (261 words)

	Citations: A Greibach normal form for context-free graph grammars - Engelfriet (ResearchIndex) (Site not responding. Last check: 2007-09-19)
		Citations: A Greibach normal form for context-free graph grammars - Engelfriet (ResearchIndex)
		J.Engelfriet; A Greibach normal form for context-free graph grammars, Proc.
		Using a result similar to the one on Apex VR graph grammars in [29] it is then not difficult to show (analogous to the method in [1] that the language is HR Pi context free.
	citeseer.ist.psu.edu /context/477088/0 (362 words)

	Formal Language Definitions
		T is a finite set of terminal symbols disjoint from V, P is a finite set of rewriting rules (productions) of the form u→w where u, w in (V∪T) S is an element of V called the start symbol.
		T is a finite set of terminal symbols disjoint from V, P is a finite set of rewriting rules (productions) of the form A→w where A∈V and w in (V∪T) S is an element of V called the start symbol.
		A grammar G = (V, T, P, S) is in Chomsky Normal Form if all the productions are of the form: variable → variable variable or variable → terminal.
	cs.wwc.edu /~aabyan/Theory/lang_def.html (1777 words)

	Entry Urbanek:1985:GNF from tcs1985.bib (Site not responding. Last check: 2007-09-19)
		Univ., Wien, Austria", keywords = "Chomsky normal form grammar; context-free grammars; derivation-oriented reasoning; Greibach normal form; Greibach normal form construction", pubcountry = "Netherlands A14", treatment = "T Theoretical or Mathematical", }
		form, 39(1)69, 39(2)297, 41(1)113, 44(2)229, 44(3)259, 47(3)299, 54(1)65, 54(2)215, 54(2)299, 60(2)177, 61(2)299, 61(2)307, 62(1)67, 64(2)203, 65(1)1, 66(3)323, 67(2)173, 68(2)135, 68(3)277
		normal, 39(2)297, 44(2)229, 44(3)259, 53(1)99, 60(2)177, 61(2)307, 62(1)67, 66(3)323, 67(2)173, 68(3)277
	www.math.utah.edu:8080 /ftp/pub/tex/bib/idx/tcs1985/40/2/315-317.html (221 words)

	Information and Computation Bibliography (Site not responding. Last check: 2007-09-19)
		In this paper, we study the complexity of deciding readiness and failure equivalences for finite state processes and recursively defined processes specified by normed context-free grammars (CFGs) in Greibach normal form (GNF).
		The results are as follows: (1) Readiness and failure equivalences for processes specified by normed GNF CFGs are both undecidable.
		For this class of processes, the regularity problem with respect to failure or readiness equivalence is also undecidable.
	theory.lcs.mit.edu /~iandc/References/huynht1995:193.html (319 words)

	Greibach-Normalform - Bedeutung, Definition, Erklärung im netlexikon
		Sie ist nach der US-Informatikerin Sheila A. Greibach benannt und beschreibt eine Normalform der kontextfreien Grammatiken, also eine Teilmenge der kontextfreien Grammatiken, die gegenüber der Menge der allgemeinen kontextfreien Grammatiken nichts an Ausdrucksstärke einbüßt.
		Jetzt können wir in allen Regeln, die zuerst auf ein Nichtterminal ableiten, die Produktionen dieses Nichtterminals einsetzen.
		Nun werden die Konstruktionsregeln auf alle Regeln von B analog angewandt.
	www.lexikon-definition.de /Greibach-Normalform.html (302 words)

	[No title] (Site not responding. Last check: 2007-09-19)
		Standard results of formal language theory tell us that for i\in\{0,2,3\} the restriction of U to lang_i still is a bi-fibration, while the restriction of U to lang_1 still is a fibration, but not a cofibration, since homomorphic images of type-1 languages need not be of type 1.
		For type-2 languages, a theorem of Greibach states the existence of a universal such, i.e., a context-free language L_{gr} such that every other context-free language is a homomorphic pre-image of L_{gr}.
		2(4) December 1973, 304--310 [HK] G"unter Hotz and Thomas Kretschmer: The power of the Greibach normal form.
	www.mta.ca /~cat-dist/catlist/1999/formallangfibres (335 words)

	581330-2 Models for Programming and Computing
		Chapter 3 of the lectures: HMU Chapters 5.1., 5.2., 5.3.1., 5.4., Greibach Normal Form p.
		423; the list of NP-complete problems given in the lectures is not to be found in the same form in the book.
		NB: Group 4 is a multilingual group, so English speakers, please attend that one.
	www.cs.helsinki.fi /u/floreen/olpe2002eng.html (523 words)

	Requirement analysis, design and verification
		Aad Mathijssen wrote a small note on exercise 8.18 in which he gives in full detail how to show two processes equivalent using CL-RSP.
		Veena Parashuram made notes on Greibach Normal Forms and on priorisation that gewis kindly put on their website (removed).
		This model exam is indicative for the final exam that will take place on thursday, January 22.
	www.win.tue.nl /~jfg/educ/2IW20/winter2004/overzicht.html (706 words)

	Citations: Ambiguity in graphs and expressions - Book, Even, Greibach, Ott (ResearchIndex) (Site not responding. Last check: 2007-09-19)
		Book, R., S. Even, S. Greibach, and G. Ott: 1971, `Ambiguity in Graphs and Expressions'.
		Book, S. Even, S. Greibach, G. Ott, "Ambiguity in Graphs and Expressions," IEEE Trans.
		, BKW98] Using these work as well as the content in two classical references [HU79, AU79] we present the following results: 1) a normal form representation for regular tree grammars, 2) a framework of marked regular expressions and model groups, and their ambiguities, 3) five subclasses of.
	citeseer.ist.psu.edu /context/641523/0 (684 words)

	CMSC 451 Lecture 15, CFG Simplification Algorithm (Site not responding. Last check: 2007-09-19)
		section 7.1 Basically: Build the set NEWV from productions of the form V -> w where V is a variable and w is one or more terminals.
		Iterate repeatedly through all productions until no change in V' or T'.
		For any production A -> w, with A in V' insert the terminals from w into the set T' and insert the variables form w into the set V' and mark the production as used.
	www.cs.umbc.edu /~squire/s01-451/cs451_l15.html (433 words)

	books - Page 1 at Think Bling
		Simple examples that explain the concepts are given.
		Chapter 2, "Context-Free Languages", introduces the pushdown automaton, which is a finite automaton that can make use of a stack containing data in a binary form.
		The term "pushdown automata" currently refers to abstract computing devices that recognize context-free languages.
	www.thinkbling.com /detail.php?ASIN=053494728X (1436 words)

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