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., Context-free grammars, differential operators and formal power series, Theoretical ... Given a context-free grammar, we can associate each formal function with an exponential formal power series. ... It also suggests the study of formal differential equations based on a context-free grammar. ...doi:10.1016/0304-3975(93)90307-f fatcat:rlgffpgbozfpviblorcny6tp4m
Lecture Notes in Computer Science
In this paper we present a coinductive definition of context free power series in terms of behavioural differential equations. ... We show that our coalgebraic approach provides a unified view on many, at first sight different, existing notions of algebraicity, and we apply our behavioural differential equations to produce a new proof ... We thank the referees for providing constructive comments and help in improving this paper. ...doi:10.1007/978-3-642-32784-1_2 fatcat:vq6hridv2fcptm6da7xl4omwd4
Rani Siromoney (6-MDRCC; Madras) 94m:68106 68Q50 05A15 Chen, William Y.C. (1-LANL; Los Alamos, NM) Context-free grammars, differential operators and formal power series. ... Given a context-free grammar, we can associate each formal function with an exponential formal power series. ...
We characterize context-free languages, and power series and streams generalizing or corresponding to the context-free languages, by means of systems of behavioural differential equations; and prove a ... differential equations yielding this sequence as a context-free stream. ... A formal power series σ is context-free if and only if there is a context-free system of behavioural differential equations, and a polynomial s ∈ S X , such that s = σ. Proof. ...doi:10.1016/j.jcss.2014.12.004 fatcat:ozzean6v55ec3lk5dvwtnvs44u
., Context-free grammars, differential operators and formal power series 117 (l-2) (1993) 113-129 Chiricota, Y., Representation symbolique d'especes moleculaires 117 (l-2) (1993) 131-136 Choffrut, C. and ... Knill 120 (1) (1993) l-44 Csuhaj-Varji, E. and A. Kelemenova, Descriptional complexity of context-free grammar forms 112 (2) (1993) 277-289 Culik II, K. and S. ...doi:10.1016/0304-3975(93)90297-7 fatcat:iseijt6oo5ed5drc4sco5bmsqq
There exist very lucid explanations of the combinatorial origins of rational and algebraic functions, in particular with respect to regular and context free languages. ... We consider several different takes on the shuffle product, shuffle closure, and shuffle grammars, and give explicit generating function consequences. ... Hollweg, and M. Rosas. We wish to also acknowledge the financial support of NSERC. ...arXiv:0802.2844v1 fatcat:w4myc64xo5ev7ntufo54hzyr5q
There exist very lucid explanations of the combinatorial origins of rational and algebraic functions, in particular with respect to regular and context free languages. ... We consider several different takes on the shuffle product, shuffle closure, and shuffle grammars, and give explicit generating function consequences. ... Hollweg, and M. Rosas. We wish to also acknowledge the financial support of NSERC. ...doi:10.4230/lipics.stacs.2008.1317 dblp:conf/stacs/MishnaZ08 fatcat:mirxwjsyzjeetidybchfkg4bmq
In this paper, the formal derivative operator defined with respect to context-free grammars is used to prove some properties about binomial coefficients and multifactorial numbers. ... In addition, we extend the formal derivative operator to matrix grammars and show that multifactorial numbers can also be generated. ... In  , formal functions and the formal derivative operator were used to study formal power series in combinatorics. ...arXiv:1808.06313v1 fatcat:zc5hibecvrctbg3pftohtqlfmi
In the present article we introduce two new combinatorial interpretations of the r-Whitney numbers of the second kind obtained from the combinatorics of the differential operators associated to the grammar ... Moreover, we show several well-known identities involving the r-Dowling polynomials and the r-Whitney numbers using the combinatorial differential calculus. ... Only derivations have a counterpart in the context of Chen grammars. The substitution rules in a context-free grammar can be translated into a differential operator. ...arXiv:1702.06519v1 fatcat:eyv6aiep6fc3fn6fatpkb46wye
International Journal on Perceptive and Cognitive Computing
Therefore, literally we can find hundreds ofstudies of well-known of various types of controlled grammars and their investigation have amount to athrilling trend within formal language theory. ... Thereby, in this paper, we briefly recapitulate the background of formallanguage theory and highlight the key results of multiset grammars, valence grammars and tree controlledgrammars. ... This situation has called for more powerful grammars with similar properties of context-free grammars known as grammars with regulated rewriting. ...doi:10.31436/ijpcc.v2i2.39 fatcat:jwoix3ktnvbvfnv6ihpbedbuda
The parallel complexity of computing context-free grammar generating series is investigated. ... It is known that this problem is in DIV, but in terms of n σ rather than n, where n is the index of the desired coefficient and σ is the grammar size. ... Details about context-free grammars and their generating series are presented in the following subsection. ...doi:10.1006/inco.2000.3023 fatcat:zqcoowvf7vfwxeyjegeiienxje
ACM SIGSAM Bulletin
Mathematical computing in a distributed environment is also becoming more plausible as libraries and computing facilities are connected with each other and with user facilities. ... Communication, storage, transmission, and searching of complex material has become increasingly important. ... Concerning T E X for CAS Communication Our view is that T E X in context and with suitable "understanding" programs, is a historically important encoding for considerable bodies of mathematics, and continues ...doi:10.1145/347127.347441 fatcat:p26nj746kzch3nty543yf25nka
We extend the Chomsky/Sch\"utzenberger method of computing the growth series of an unambiguous context-free language to the larger class of indexed languages. ... The third author offers thanks to Mike Zabrocki and the participants of the Algebraic Combinatorics seminar at the Fields Institute for Research in Mathematical Science (Toronto, Canada) for early discussions ... For each production, replace each terminal with the formal variable z and each non-terminal A with a formal power series A(z). ...doi:10.1051/ita/2013041 fatcat:syf5uxsxmrgcbhil2sdgeimjwq
represented as a context-free grammar, named level grammar, for the first time. ... Specifically, perception cube and decision spheroid are visually represented as context-free grammars, named fusion grammar and synthesis grammar, respectively. ... This observation follows directly from the known property that the union of a finite number of context-free grammars is also a context-free one. ...doi:10.1109/3468.983413 fatcat:g5wdfexocbeivn4vrkialjffau
This is a generalization to a countable set of variables of the notion of context-free grammar. (3) To each formal schema is associated a system of formal equa- tions one of whose solutions in the ring ... Author’s summary: “A formal power series = f(n)x” is said to be differentiably finite if it satisfies a linear differential equation with polynomial coefficients. ...
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