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Page 4679 of Mathematical Reviews Vol. , Issue 83k [page]

1983 Mathematical Reviews  
Huynh Thiet-Dung 83k:68072 Remarks on the complexity of an invariant of context-free grammars. Acta Inform. 17 (1982), no. 1, 89-99.  ...  The paper poses the question of the decidability of whether an IRS context-free language is linear context-free. S. A.  ... 

A COMPLEX MEASURE FOR LINEAR GRAMMARS

Ishanu Chattopadhyay, Asok Ray
2005 Demonstratio Mathematica  
As a step toward achieving this goal, this paper introduces a complex measure of linear context free grammars (LCFG) that belong to the class of non-regular languages.  ...  The proposed complex measure becomes equivalent to the signed reed measure, reported in recent literature, if the LCFG is degenerated to a regular grammar. 1991 Mathematics Subject Classification: 93A05  ...  Then, it extends the signed real measure of regular languages to a complex measure for the class of non-regular languages [1] , generated by the (deterministic) linear context free grammar (LCFG) that  ... 
doi:10.1515/dema-2005-0323 fatcat:wp4q4gl2p5c5np7firujm3a37a

Commutative grammars: The complexity of uniform word problems

Dung T. Huynh
1983 Information and Control  
Commutative grammars are introduced, and various classes of commutative grammars are defined. The complexity of uniform word problems for commutative grammars is investigated.  ...  Estenfeld for reading the manuscript, and an anonymous referee for helpful advice in clarifying the presentation of this paper. RECEIVED: June 25, 1982; REVISED: August 6, 1983  ...  ACKNOWLEDGMENTS The author wishes to thank Professor G. Hotz for many suggestions, B. Becker and K.  ... 
doi:10.1016/s0019-9958(83)80022-9 fatcat:mhvhe6q7yvhoviyfpdsu2nb5yy

Page 4810 of Mathematical Reviews Vol. , Issue 86j [page]

1986 Mathematical Reviews  
Author summary: “The Hotz group H(G) = F(V UX)/P of a reduced context-free grammar G = (V,X,P,S) depends on the generated language L only [G. Hotz, Theoret. Comput.  ...  Here, a control language with respect to an arbitrary grammar G for the recursively enumerable language L is generated by a linear grammar G’ with only one variable, and the validity of the sequence of  ... 

Compressing Permutation Groups into Grammars and Polytopes. A Graph Embedding Approach [article]

Lars Jaffke, Mateus de Oliveira Oliveira, Hans Raj Tiwary
2020 arXiv   pre-print
In this work, we show that the minimum size of a context-free grammar generating a finite permutation group G S_n can be upper bounded by three structural parameters of connected graphs embedding G: the  ...  In particular, by combining our main result with a celebrated 2^Ω(n) lower bound on the grammar complexity of the symmetric group S_n we have that connected graphs of treewidth o(n/log n) and maximum degree  ...  We thank Michel Goemans, Kanstantsin Pashkovich and Stefan Weltge for answering some of our questions by email.  ... 
arXiv:2001.05583v1 fatcat:7jzmxff5drhynmaqvxthz4q4pe

Compressing Permutation Groups into Grammars and Polytopes. A Graph Embedding Approach

Lars Jaffke, Mateus de Oliveira Oliveira, Hans Raj Tiwary, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
In this work, we show that the minimum size of a context-free grammar generating a finite permutation group G⊑ 𝕊_n can be upper bounded by three structural parameters of connected graphs embedding G:  ...  In particular, by combining our main result with a celebrated 2^{Ω(n)} lower bound on the grammar complexity of the symmetric group 𝕊_n due to Glaister and Shallit [Glaister and Shallit, 1996] we have  ...  We thank Michel Goemans, Kanstantsin Pashkovich and Stefan Weltge for answering some of our questions by email.  ... 
doi:10.4230/lipics.mfcs.2020.50 dblp:conf/mfcs/JaffkeOT20 fatcat:chhzsevisfdjxjihsgn346opq4

Parsing for semidirectional Lambek Grammar is NP-complete

Jochen Dörre
1996 Proceedings of the 34th annual meeting on Association for Computational Linguistics -  
We study the computational complexity of the parsing problem of a variant of Lambek Categorial Grammar that we call semidirectional.  ...  SD[ grammars are able to generate each context-free language and more than that.  ...  Whereas Lambek grammars generate exactly the context-free languages (modulo the missing empty word) (Pentus 93), the latter generate all permutation closures of context-free languages (Benthem 88).  ... 
doi:10.3115/981863.981876 dblp:conf/acl/Dorre96 fatcat:wbj2ibld3rgsjlb2rvmkra7hxi

THE INCLUSION PROBLEM OF CONTEXT-FREE LANGUAGES: SOME TRACTABLE CASES

ALBERTO BERTONI, CHRISTIAN CHOFFRUT, ROBERTO RADICIONI
2011 International Journal of Foundations of Computer Science  
We study the problem of testing whether a context-free language is included in a fixed set L0, where L0 is the language of words reducing to the empty word in the monoid defined by a complete string rewrite  ...  As an application, we obtain a polynomial time algorithm for testing if a context-free language is included in a Dyck language (the best previous algorithm for this problem was doubly exponential).  ...  An open problem on 2-homogeneous rewrite systems is to study the precise complexity of Inclusion Problem in the non N -free case; moreover, it would be interesting to identify complete unitary rewrite  ... 
doi:10.1142/s0129054111008040 fatcat:iqu2fcconbcepmuly67ezyao3u

Parsing for Semidirectional Lambek Grammar is NP-Complete [article]

Jochen Doerre
1996 arXiv   pre-print
We study the computational complexity of the parsing problem of a variant of Lambek Categorial Grammar that we call semidirectional.  ...  non-peripheral extraction. grammars are able to generate each context-free language and more than that.  ...  Whereas Lambek grammars generate exactly the context-free languages (modulo the missing empty word) (Pentus 93), the latter generate all permutation closures of context-free languages (Benthem 88).  ... 
arXiv:cmp-lg/9605016v1 fatcat:vixb6kltonhinkfbhnkgyw5fe4

Coding-theorem Like Behaviour and Emergence of the Universal Distribution from Resource-bounded Algorithmic Probability [article]

Hector Zenil, Liliana Badillo, Santiago Hernández-Orozco, Francisco Hernández-Quiroz
2018 arXiv   pre-print
may shed light on the distribution of outcomes.  ...  In the context of natural processes that operate below the Turing universal level because of finite resources and physical degradation, the investigation of natural biases stemming from algorithmic rules  ...  Type-2 Grammars that generate the context-free languages. These kinds of grammars are extensively used in linguistics.  ... 
arXiv:1711.01711v11 fatcat:5o6zzw44fjfwfdjt35x7wrxyva

Querying for Paths in Graphs using Context-Free Path Queries [article]

Jelle Hellings
2016 arXiv   pre-print
For the all-path query semantics, we show that the result of a query can be represented by a finite context-free grammar annotated with node-information relevant for deriving each path in the query result  ...  While focusing on context-free path queries, we provide a formal framework for evaluating queries on graphs using both path-based query semantics.  ...  As annotated grammars are context-free grammars, one can use existing context-free enumeration techniques [11, 15, 12, 25] to produce some of the paths represented by the annotated grammar.  ... 
arXiv:1502.02242v2 fatcat:ndt2ybgf7jhvvpb3jksrhnpw4a

Quantum grammars

V. A. Malyshev
2000 Journal of Mathematical Physics  
We consider quantum (unitary) continuous time evolution of spins on a lattice together with quantum evolution of the lattice itself.  ...  It is also related to what is called quantum circuits, one of the incarnations of a quantum computer. We consider simpler models for which one can obtain exact mathematical results.  ...  If L is not assumed to be symmetric then one can define context free grammars, see [8] (but there are no nontrivial symmetric context free grammars) A context free grammar is one where all α i have length  ... 
doi:10.1063/1.533357 fatcat:5dy4ayapojdivjoufl2up3purm

Page 1293 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
, How to generate binary codes using context-free grammars (289-301).  ...  languages over the binary alphabet (181- 188); Lucian Ilie, On generalized slenderness of context-free lan- guages (189-202); Teruo Imaoka, Prehomomorphisms on locally inverse *-semigroups (203-209); Florentin  ... 

Geometrical methods for the theory of linear systems

Mark A. Shayman
1982 Computers and Mathematics with Applications  
Chapter 3 starts with the notion of a grammar and develops the natural correspondence between context-free languages, context-free grammars, and pushdown automata.  ...  Important properties of the context-free languages are derived; this leads into an excellent discussion of parsing techniques. Moving down the Chomsky hierarchy, Chapter 4 concerns Turing machines.  ...  This book is an edited compilation of tutorial lectures on applications of commutative algebra, algebraic geometry, and differential geometry to the theory of time-invariant linear systems.  ... 
doi:10.1016/0898-1221(82)90048-7 fatcat:7dyjp7jztzb2njdsvjhctj4w4e

An efficient all-parses systolic algorithm for general context-free parsing

Oscar H. Ibarra, Michael A. Palis
1990 International journal of parallel programming  
The problem of outputting all parse trees of a string accepted by a context-free grammar is considered.  ...  Comments .Abstract: The problem of outputting all parse trees of a string accepted by a context-free grammar is considered.  ...  Complexity Analysis Since the underlying context-free grammar is in Chornsky normal form, every parse tree has size (number of nodes) 2n-1, where n is the length of the input string.  ... 
doi:10.1007/bf01379361 fatcat:gwufnqqkfrd7zgvcch6c2kew2e
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