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Vector symbolic architectures for context-free grammars [article]

Peter beim Graben, Markus Huber, Werner Meyer, Ronald Römer, Matthias Wolff
2020 arXiv   pre-print
We define a novel 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)  ... 
arXiv:2003.05171v2 fatcat:e4unrz4ehzenbhnfx6lm2leyvq

Generating all permutations by context-free grammars in Chomsky normal form

Peter R.J. Asveld
2006 Theoretical Computer Science  
Let L n be the finite language of 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.  ... 
doi:10.1016/j.tcs.2005.11.010 fatcat:ruufccqtnngdtphttdtgxxtw64

Cyclic Shift on Multi-component Grammars [chapter]

Alexander Okhotin, Alexey Sorokin
2020 Lecture Notes in Computer Science  
Multi-component 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).  ... 
doi:10.1007/978-3-030-40608-0_20 fatcat:4mvghvfawnhqpbqtieak7ekg2q

GENERATING ALL CIRCULAR SHIFTS BY CONTEXT-FREE GRAMMARS IN GREIBACH NORMAL FORM

PETER R. J. ASVELD
2007 International Journal of Foundations of Computer Science  
We study a few families of 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  ... 
doi:10.1142/s0129054107005182 fatcat:gg4rjfdm4zggffy5orhssh5vo4

Splicing systems and the Chomsky hierarchy

Jean Berstel, Luc Boasson, Isabelle Fagnot
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.  ... 
doi:10.1016/j.tcs.2012.03.008 fatcat:llyu7onjxna5xbfiop6u2ff6na

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

Peter R.J. Asveld
2008 Theoretical Computer Science  
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.  ...  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.  ... 
doi:10.1016/j.tcs.2008.09.033 fatcat:4n3twmx46fbvrpbwx54qzbwypm

Splicing systems and the Chomsky hierarchy [article]

Jean Berstel, Luc Boasson, Isabelle Fagnot
2011 arXiv   pre-print
Second, we prove the language 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.  ... 
arXiv:1102.0947v1 fatcat:onsxjbqxnrbwzdy7jyv66ndrbu

Passes and paths of attribute grammars

Joost Engelfriet, Gilberto Filè
1981 Information and Control  
There is no requirement, as for the usual multi-pass attribute 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  ... 
doi:10.1016/s0019-9958(81)90466-6 fatcat:fxbkiadgx5bzro4cdbno5gpsfy

Formalism, grammatical rules, and normativity [chapter]

Geoffrey K. Pullum
2019 Zenodo  
Syntactic theory has been dominated 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.  ... 
doi:10.5281/zenodo.2654367 fatcat:rglbqhnjcfcxfechikkkvbxnyu

Conjunctive and Boolean grammars: The true general case of the context-free grammars

Alexander Okhotin
2013 Computer Science Review  
Conjunctive 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  ... 
doi:10.1016/j.cosrev.2013.06.001 fatcat:vjrnokycqres5mfpdupksfaumm

Applications of fuzzy languages and pictorial databases to decision support systems design

Edward T. Lee
1983 Proceedings of the May 16-19, 1983, national computer conference on - AFIPS '83  
First, fuzzy languages, fuzzy 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  ... 
doi:10.1145/1500676.1500732 dblp:conf/afips/Lee83 fatcat:jjyktogu4nhgtoeir7jvmrlppy

Converting Nondeterministic Automata and Context-Free Grammars into Parikh Equivalent One-Way and Two-Way Deterministic Automata [article]

Giovanna J. Lavado, Giovanni Pighizzini, Shinnosuke Seki
2012 arXiv   pre-print
Concerning 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.  ... 
arXiv:1212.1346v2 fatcat:who6tp34izcmfav3acvw5en6mu

The generative power of rule orderings in formal grammars

FRANCIS JEFFRY PELLETIER
1980 Linguistics  
Another way is the G-view: disallow certain 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.  ... 
doi:10.1515/ling.1980.18.1-2.17 fatcat:4pzmpyfmlbfnheut4bmsfnjcgu

An optimized parsing algorithm well suited to RNA folding

F Lefebvre
1995 Proceedings. International Conference on Intelligent Systems for Molecular Biology  
The application of stochastic 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.  ... 
pmid:7584441 fatcat:uasx7rllpjeppeaexlqssa44dy

On 'the Galilean style' of linguistic inquiry

Rudolf P. Botha
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.  ... 
doi:10.1016/0024-3841(82)90056-0 fatcat:is25iaw3h5falm3sdtbyps76a4
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