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Vector symbolic architectures for context-free grammars
[article]

2020
*
arXiv
*
pre-print

We define a novel

arXiv:2003.05171v2
fatcat:e4unrz4ehzenbhnfx6lm2leyvq
*normal**form*for CFG*by*means of term algebras. ... We present a rigorous mathematical framework for the representation of phrase structure trees and parse trees of*context*-*free**grammars*(CFG)*in*Fock space, i.e. infinite-dimensional Hilbert space as being ... The phrase structure tree Fig. 2 immediately gives rise to a*context*-*free**grammar*(CFG)*by*interpreting every branch as a rewriting rule*in**Chomsky**normal**form*[51, 29] S → NP VP (3a) NP → D N (3b) ...##
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Generating all permutations by context-free grammars in Chomsky normal form

2006
*
Theoretical Computer Science
*

Let L n be the finite language of

doi:10.1016/j.tcs.2005.11.010
fatcat:ruufccqtnngdtphttdtgxxtw64
*all*n! strings that are permutations of n different symbols (n ≥ 1). We consider*context*-*free**grammars*G n*in**Chomsky**normal**form*that*generate*L n . ...*In*particular we study a few families {G n } n≥1 , satisfying L(G n ) = L n for n ≥ 1, with respect to their descriptional complexity, i.e. we determine the number of nonterminal symbols and the number ... For each n ≥ 1, G 2 n is an unambiguous*context*-*free**grammar**in**Chomsky**normal**form*. Proof.*By*Definition 5.4, G 2 n is a*context*-*free**grammar**in**Chomsky**normal**form*. ...##
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Cyclic Shift on Multi-component Grammars
[chapter]

2020
*
Lecture Notes in Computer Science
*

Multi-component

doi:10.1007/978-3-030-40608-0_20
fatcat:4mvghvfawnhqpbqtieak7ekg2q
*grammars*, known*in*the literature as "multiple*context*-*free**grammars*" and "linear*context*-*free*rewriting systems", describe the structure of a string*by*defining the properties of k-tuples ... of its substrings,*in*the same way as ordinary formal*grammars*(Chomsky's "*context*-*free*") define properties of substrings. ... A well-nested multi-component*grammar*can be transformed to the following*form*resembling the*Chomsky**normal**form*. Proposition 1. ([15], Thm. 1). ...##
###
GENERATING ALL CIRCULAR SHIFTS BY CONTEXT-FREE GRAMMARS IN GREIBACH NORMAL FORM

2007
*
International Journal of Foundations of Computer Science
*

We study a few families of

doi:10.1142/s0129054107005182
fatcat:gg4rjfdm4zggffy5orhssh5vo4
*context*-*free**grammars*G n (n ≥ 1)*in*Greibach*normal**form*such that G n*generates*C n . ... As*in*the case of*Chomsky**normal**form*, these ν, π and δ are functions bounded*by*low-degree polynomials. ... Satta [15] conjectured that "any*context*-*free**grammar*G n*in**Chomsky**normal**form*(CNF) that*generates*L n must have a number of nonterminal symbols that is not bounded*by*any polynomial function*in*n ...##
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Splicing systems and the Chomsky hierarchy

2012
*
Theoretical Computer Science
*

*In*this paper, we prove decidability properties and new results on the position of the family of languages

*generated*

*by*(

*circular*) splicing systems within the

*Chomsky*hierarchy. ... Second, we prove the language

*generated*

*by*an alphabetic splicing system is

*context*-

*free*. ... A theorem on

*generalized*

*context*-

*free*

*grammars*For sake of completeness, we give here a proof of Theorem 6.1, together with an example. ...

##
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Generating all permutations by context-free grammars in Greibach normal form

2008
*
Theoretical Computer Science
*

We consider

doi:10.1016/j.tcs.2008.09.033
fatcat:4n3twmx46fbvrpbwx54qzbwypm
*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. ... Recall that a λ-*free**context*-*free**grammar*G = (V , Σ, P, S) is*in**Chomsky**normal**form*(CNF) if P ⊆ N ×(N −{S}) 2 ∪N ×Σ where N = V − Σ. ...##
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Splicing systems and the Chomsky hierarchy
[article]

2011
*
arXiv
*
pre-print

Second, we prove the language

arXiv:1102.0947v1
fatcat:onsxjbqxnrbwzdy7jyv66ndrbu
*generated**by*an alphabetic splicing system is*context*-*free*. ...*In*this paper, we prove decidability properties and new results on the position of the family of languages*generated**by*(*circular*) splicing systems within the*Chomsky*hierarchy. ... The*grammar*G is said to be a*generalized**context*-*free**grammar*461 if the languages M v are*all**context*-*free*. 462 Derivations are defined as usual. ...##
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Passes and paths of attribute grammars

1981
*
Information and Control
*

There is no requirement, as for the usual multi-pass attribute

doi:10.1016/s0019-9958(81)90466-6
fatcat:fxbkiadgx5bzro4cdbno5gpsfy
*grammars*, that*all*occurrences of the same attribute are computed*in*the same pass, R is shown that the problem of determining whether an ... A*general*result on dependency paths of attribute*grammars*relates them to (finite-copying) top-down tree transducers. The formal power of k-pass attribute*grammars*increases with increasing k. ... We thank Erik Meineche Schmidt and Sven Skyum for pointing out the relevance of*Chomsky**Normal**Form*for attribute*grammars*. RECEIVED: February 12, 1981; REVISED: July 23, 1981 ...##
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Formalism, grammatical rules, and normativity
[chapter]

2019
*
Zenodo
*

Syntactic theory has been dominated

doi:10.5281/zenodo.2654367
fatcat:rglbqhnjcfcxfechikkkvbxnyu
*by*the*generative*conception for six decades. ... Despite reference*in*the literature to "rules",*generative**grammars*do not contain rules*in*the usual sense (under which a rule can be followed or disobeyed). ... We are*in*effect giving a formally explicit model for a*context*-*free*language without using a*context*-*free**generative**grammar*. ...##
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Conjunctive and Boolean grammars: The true general case of the context-free grammars

2013
*
Computer Science Review
*

Conjunctive

doi:10.1016/j.cosrev.2013.06.001
fatcat:vjrnokycqres5mfpdupksfaumm
*grammars*extend the definition of a*context*-*free**grammar**by*allowing a conjunction operation*in*the rules; Boolean*grammars*are further equipped with an explicit negation. ... These*grammars*maintain the main principle of the*context*-*free**grammars*, that of defining syntactically correct strings inductively from their substrings, but lift the restriction of using disjunction ... The first of them is a direct*generalization*of the*Chomsky**normal**form*of*context*-*free**grammars*,*in*which every rule is either of the*form*A → BC with B, C ∈ N , or of the*form*A → a with a ∈ Σ, with ...##
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Applications of fuzzy languages and pictorial databases to decision support systems design

1983
*
Proceedings of the May 16-19, 1983, national computer conference on - AFIPS '83
*

First, fuzzy languages, fuzzy

doi:10.1145/1500676.1500732
dblp:conf/afips/Lee83
fatcat:jjyktogu4nhgtoeir7jvmrlppy
*grammars*, the classification of fuzzy*grammars*, derivation chain, degree of acceptance, and equivaience are defined. ... Second, algebraic representation of the production system is presented and illustrated*by*examples. The difference between null string and the empty set of string is illustrated. ... This has been done for the notions of*grammar*, Kleene closure, recursiveness,*context*-sensitive languages,*context*-*free*languages, regular languages,*Chomsky**normal**form*, Greibach*normal**form*, and so on ...##
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Converting Nondeterministic Automata and Context-Free Grammars into Parikh Equivalent One-Way and Two-Way Deterministic Automata
[article]

2012
*
arXiv
*
pre-print

Concerning

arXiv:1212.1346v2
fatcat:who6tp34izcmfav3acvw5en6mu
*context*-*free**grammars*, we prove that for each*grammar**in**Chomsky**normal**form*with h variables there exist Parikh equivalent one-way and two-way deterministic automata with 2^O(h^2) and 2^O(h ...*In*contrast, if*all*the words accepted*by*the given automaton contain at least two different letters, then a Parikh equivalent one-way deterministic automaton with a polynomial number of states can be ...*In*particular, Theorem 5.3 is due to him. Many thanks also to Jeff Shallit who suggested to add Example 3.1. ...##
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The generative power of rule orderings in formal grammars

1980
*
Linguistics
*

Another way is the G-view: disallow certain

doi:10.1515/ling.1980.18.1-2.17
fatcat:4pzmpyfmlbfnheut4bmsfnjcgu
*grammars*, regardless of whether this results*in*a reduction of*generative*capacity. ... as powerful*in*strong*generative*capacity as rule ordering theory A. ... When looked at this way, PS rules*form*a*context*-*free**grammar*with initial symbol S. ...##
###
An optimized parsing algorithm well suited to RNA folding

1995
*
Proceedings. International Conference on Intelligent Systems for Molecular Biology
*

The application of stochastic

pmid:7584441
fatcat:uasx7rllpjeppeaexlqssa44dy
*context*-*free**grammars*to the determination of RNA foldings allows a simple description of the sub-class of sought secondary structures, but it needs efficient parsing algorithms ... The more classic thermodynamic model of folding, popularized*by*Zuker under the framework of dynamic programming algorithms, allows an easy computation of foldings but its use is delicate when constraints ... Some of the modifications required*by*the algorithm to handle stochastic*grammars*(which are not*in**Chomsky**normal**form*) do not improve efficiency, to say the least. ...##
###
On 'the Galilean style' of linguistic inquiry

1982
*
Lingua
*

*In*a different

*context*, however,

*Chomsky*(1979a) deals more explicitly with the question of the relationship between

*generative*

*grammar*and mathematics. ... style" as a new mode of inquiry

*in*

*generative*

*grammar*. ...

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