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Context-Free Languages and Pushdown Automata
[chapter]
1997
Handbook of Formal Languages
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It is in cubic double Greibach normal form (resp. in quadratic double Greibach normal form i it is in double Greibach normal form and each right member of a rule contains at most 3 variables (resp. at ...
, we get an equivalent grammar which is now in quadratic double Greibach normal form. ...
Index "-rule, 3 bracket operation, 49 Chomsky normal form, 15 Chomsky-Sch utzenberger's theorem, 25 ...
doi:10.1007/978-3-642-59136-5_3
fatcat:5ikmp6unurdwbl773xucv4v3ni
Generating all permutations by context-free grammars in Greibach normal form
2008
Theoretical Computer Science
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We consider context-free grammars G n in Greibach normal form and, particularly, in Greibach m-form (m = 1, 2) which generates the finite language L n of all n! ...
As in the case of Chomsky normal form, these descriptional complexity measures grow faster than any polynomial function. ...
This straightforward approach is no longer possible when we require that the context-free grammar possesses a special form, such as Chomsky normal form (CNF) or Greibach normal form (GNF). ...
doi:10.1016/j.tcs.2008.09.033
fatcat:4n3twmx46fbvrpbwx54qzbwypm
Context-free grammars with cancellation properties
1985
Theoretical Computer Science
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If in addition the grammar is not derivation-bounded, then the language generated is a generator of the family of context-free languages. ...
Given a context-free grammar G the Hotz monoid (group) of G is the quotient of the free monoid (group) on the alphabet by the relations defined by the productions. ...
First, note that if Pl =(v, m), then mv -~ is cyclically reduced, since G is on double Greibach form. We examine the different cases for p~" (1) The rule p~ has the form v~xc with xc~X¢. ...
doi:10.1016/0304-3975(85)90127-6
fatcat:orypjo6ubvcojjzazd7poddinq
Higher-order Context-free Session Types in System F
2022
Electronic Proceedings in Theoretical Computer Science
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2022 pre-print arXiv:2203.12877v1 fatcat:hq3wloidgng7xcyh6e2zjwvvji
We present an extension of System F with higher-order context-free session types. ...
We present three notions of type equivalence: a syntactic rule-based version, a semantic bisimulation-based version, and an algorithmic version by reduction to the problem of bisimulation of simple grammars ...
expressive than grammars in Greibach normal form. ...
doi:10.4204/eptcs.356.3
fatcat:r3ui7ktm75amdg6mjibqak4hne
Sequential grammars and automata with valences
2002
Theoretical Computer Science
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Chomsky and Greibach normal form theorems and an iteration lemma for context-free valence grammars over the groups Z k are proved. The generative power of di erent control monoids is investigated. ...
Proposition 5.12 (Chomsky normal form). For any context-free valence grammar G over Z k ; there is an equivalent context-free valence grammar G over Z k with core rules of the form A → BC; A → a. ...
With some additional e ort, other normal forms, e.g., a quadratic double Greibach normal form, could be shown for L(Val; CF; Z k ). ...
doi:10.1016/s0304-3975(01)00282-1
fatcat:az4zrslmvjc7fkwcihn7g5sxem
Prefix Lexicalization of Synchronous CFGs using Synchronous TAG
2018
Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
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Our results extend Greibach normal form from CFGs to SCFGs and prove new formal properties about SCFG, a formalism with many applications in natural language processing. ...
This transformation at most doubles the grammar's rank and cubes its size, but we show that in practice the size increase is only quadratic. ...
We dedicate this paper to the memory of Prof. Aravind Joshi; a short hallway conversation with him at ACL 2014 was the seed for this paper. ...
doi:10.18653/v1/p18-1107
dblp:conf/acl/SarkarB18
fatcat:p3je3mjwl5dwfaoq4mqitqsxhe
Action Logic is Undecidable
[article]
2019
arXiv
pre-print
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Action logic is the algebraic logic (inequational theory) of residuated Kleene lattices. This logic involves Kleene star, axiomatized by an induction scheme. ...
Decidability of action logic itself was an open question, raised by D. Kozen in 1994. In this article, we show that it is undecidable, more precisely, Σ_1^0-complete. ...
Now we are ready to construct G M,x , which is going to be a context-free grammar in Greibach [15] normal form. ...
arXiv:1912.11273v1
fatcat:3fcadczxtvdkxoufcj3jfy2txq
String adjunct grammars: II. Equational representation, null symbols, and linguistic relevance
1972
Information and Control
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in X~ are elementary sentence forms and not elementary sentences), and for every w EL(G) there is an elementary sentence underlying it (for different readings of an ambiguous w the underlying elementary ...
Elementary Sentences (Elementary Sentence Forms) In an A G G the set of strings in Xc can be considered as elementary sentences (in the linguistic context symbols in A are category symbols and hence strings ...
doi:10.1016/s0019-9958(72)80005-6
fatcat:ga2ofuwtr5gijf5nn6ghesifla
The hardest language for grammars with context operators
[article]
2021
arXiv
pre-print
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normal form. ...
An essential step of the argument is a new normal form for grammars with context operators, in which every nonterminal symbol defines only strings of odd length in left contexts of even length: the even-odd ...
Greibach's proof of her hardest language theorem for ordinary grammars essentially uses the Greibach normal form, with all rules of the form A → aα, where a is a symbol of the alphabet. ...
arXiv:2012.03596v2
fatcat:qzzdfl2tdrg7jnesrbigick7yq
Equivalences and transformations of regular systems—Applications to recursive program schemes and grammars
1986
Theoretical Computer Science
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This work presents a unified theory of recursive program schemes, context-free grammars, grammars on arbitrary algebraic structures and, in fact, recursive definitions of all kind by means of regular systems ...
The equivalences of regular systems associated with either all their solutions or their least solutions (in all domains of appropriate type satisfying a set of algebraic laws expressed by equations) are ...
Greibach normal form The construction which transforms an arbitrary context-free grammar G into an equivalent one G' in Greibach normal form is more complicated. ...
doi:10.1016/0304-3975(86)90050-2
fatcat:kpme4cdkorgohh7556pyx47emy
Families of automata characterizing context-sensitive languages
2005
Acta Informatica
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In the hierarchy of infinite graph families, rational graphs are defined by rational transducers with labelled final states. ...
Let Gr be a grammar in Greibach normal form generating L Lin from a non-terminal S. ...
elementary relations of the form R.S where R ∈ Rat((Σ × Σ) * ) and S ∈ Dif Rat . ...
doi:10.1007/s00236-004-0160-0
fatcat:bipfh4il45es5dy3447pb2bxui
Conjunctive and Boolean grammars: The true general case of the context-free grammars
2013
Computer Science Review
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open problems, with an award offered for the first correct solution of each problem. ...
The paper is also addressed to theoretical computer scientists seeking a subject for research; an account of pure theoretical research in the area presented in this paper is accompanied by a list of significant ...
: S → aA (a ∈ Σ, A ∈ N ) S → ε For ordinary context-free grammars, there is another important normal form: the Greibach normal form [34] , in which every rule is either A → aα with a ∈ Σ and α ∈ (Σ ∪ ...
doi:10.1016/j.cosrev.2013.06.001
fatcat:vjrnokycqres5mfpdupksfaumm
Complexity of the Infinitary Lambek Calculus with Kleene Star
[article]
2020
arXiv
pre-print
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We consider the Lambek calculus, or non-commutative multiplicative intuitionistic linear logic, extended with iteration, or Kleene star, axiomatised by means of an ω-rule, and prove that the derivability ...
Acknowledgments The author is grateful to the organisers and participants of WoLLIC 2017 and MIAN-POMI 2018 Winter Session on Mathematical Logic for fruitful discussions and friendly atmosphere. ...
Consider a language without the empty word generated by a context-free grammar G in Greibach normal form (Greibach, 1965) . ...
arXiv:2005.00404v1
fatcat:iee42aq7efctnhooi56qvh4ude
Pushdown automata, multiset automata, and Petri nets
2001
Theoretical Computer Science
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In particular, we provide a proof of an earlier conjecture by Moller: that multiset automata form a proper subset of Petri nets. ...
We provide example automata which demonstrate the strictness of this hierarchy. ...
BPA represents the class of Basic Process Algebra processes of Bergstra and Klop [4] , which are the transition systems associated with Greibach normal form (GNF) context-free grammars in which only left-most ...
doi:10.1016/s0304-3975(00)00099-2
fatcat:xmpdbo5g5vailiuuarvb5mhole
An analysis of fixed-point queries on binary trees
1991
Theoretical Computer Science
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., An analysis of fixed-point queries on binary trees, Theoretical Computer Science 85 (1991) 75-95. ...
The presence of ordering appears to play an essential role in the logical expressibility of polynomialtime queries on finite structures. ...
He thanks both of his advisors, Sheila Greibach and Yiannis Moschovakis, for their time and patience. ...
doi:10.1016/0304-3975(91)90048-7
fatcat:qv2rbd3aqfa4daoypfcg7m5dm4
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