... grammars
and observe that they are a context-free rewriting sys-
tem.
Linear Context-Free RewritingSystems
Linear context-free rewritingsystems arose from the
observation that a number ... lin-
ear context-free rewriting systems. This paper shows
how the class of string languages generated by linear
context-free rewritingsystems relates to a number of
other systems that have been ... linear context-
free rewritingsystems and multicomponent tree ad-
joining grammars [6] generate the same string lan-
guages. The multiple context-free grammars of [7] are
equivalent to linear...
... Negra corpus.
Translation: After that coal dust had caught fire.
2 Linear Context-Free Rewriting
Systems
Linear Context-Free RewritingSystems (LCFRS;
Vijay-Shanker et al., 1987; Weir, 1988) subsume
a ... Proceedings of IWPT, pages 104–
116.
Daniel Gildea. 2010. Optimal parsing strategies
for linear context-free rewriting systems. In
Proceedings of NAACL HLT 2010., pages 769–
776.
Carlos G
´
omez-Rodr
´
ıguez, ... G
´
omez-Rodr
´
ıguez, Marco Kuhlmann, and
Giorgio Satta. 2010. Efficient parsing of well-
nested linear context-free rewriting systems. In
Proceedings of NAACL HLT 2010., pages 276–
284.
Carlos G
´
omez-Rodr
´
ıguez,...
... Independent
parallelism in finite copying parallel rewriting sys-
tems. Theoretical Computer Science, 223:87–120.
Giorgio Satta. 1992. Recognition of linear context-free
rewriting systems. In Proceedings of the ... of Information Engineering
University of Padua, Italy
satta@dei.unipd.it
Abstract
Linear Context-Free Rewriting Systems
(LCFRSs) are a grammar formalism ca-
pable of modeling discontinuous phrases.
Many ... run-
ning time improvement for known parsing
algorithms for this class.
1 Introduction
Linear Context-Free Rewriting Systems
(LCFRSs) have been introduced by Vijay-
Shanker et al. (1987) for modeling...
... conswained
grammatical systems, and defined a class of such
systems called Linear Context-Free RewritingSystems
(LCFRS's). LCFRS's are constrained to have linear non-
erasing composition ... as a
279
COMBINATORY CATEGORIAL GRAMMARS: GENERATIVE POWER AND
RELATIONSHIP TO LINEAR CONTEXT-FREE REWRITING SYSTEMS& quot;
David J. Weir
Aravind K. Joshi
Department of Computer and Information ... Categorial Grammars and com-
pare them to those of grammar formalisms in the class of
Linear Context-Free Rewriting Systems. We also discuss
certain extensions of CombinaWry Categorial Grammars
and...
... copying parallel rewriting sys-
tems. Theor. Comput. Sci., 223(1-2):87–120.
Beno
ˆ
ıt Sagot and Giorgio Satta. 2010. Optimal rank re-
duction for linear context-free rewritingsystems with
fan-out ... G
´
omez-Rodr
´
ıguez, Marco Kuhlmann, and Gior-
gio Satta. 2010. Efficient parsing of well-nested linear
context-free rewriting systems. In Proc. 2010 Meeting
of the North American chapter of the Association for
Computational ... Linguistics,
35(4):559–595.
Laura Kallmeyer and Wolfgang Maier. 2010. Data-
driven parsing with probabilistic linear context-free
rewriting systems. In Proc. 23rd International Con-
ference on Computational Linguistics (Coling...
... 2-7 August 2009.
c
2009 ACL and AFNLP
An Optimal-Time Binarization Algorithm
for Linear Context-Free RewritingSystems with Fan-Out Two
Carlos G
´
omez-Rodr
´
ıguez
Departamento de Computaci
´
on
Universidade ... of Information Engineering
University of Padua, Italy
satta@dei.unipd.it
Abstract
Linear context-free rewriting systems
(LCFRSs) are grammar formalisms with
the capability of modeling discontinu-
ous ... much effort to the development
of formal systems for modeling the syntax of nat-
ural language. There has been a considerable in-
terest in rewritingsystems that enlarge the generat-
ive power...
... r. Then
each elementary step in the recognition of Pl can
93
RECOGNITION OF
LINEAR CONTEXT-FREE REWRITING SYSTEMS*
Giorgio Satta
Institute for Research in Cognitive Science
University ... for linear context-free
rewriting languages.
1 INTRODUCTION
Beginning with the late 70's, there has been a consid-
erable interest within the computational linguistics
field for rewriting ... in [Vijay-
Shanker
et al.,
1987] and [Weir, 1988] with the in-
troduction of linear context-free rewritingsystems
(LCFRS) and in [Kasami
et al.,
1987] and [Seki
et
a/., 1989] with the...
... Agarwal, M Bohner, P Rehak, Half -linear dynamic equations. Nonlinear
Anal. Appl. 1, 1–56 (2003)
[8] LQ Jiang, Z Zhou, Lyapunov inequality for linear Hamiltonian systems on
time scales. J. Math. ... Lyapunov for linear Hamil-
tonian systems on time scales. J. Math. Anal. Appl. 381, 695–705 (2011)
[11] GSh Guseinov, B Kaymakcalan, Lyapunov inequalities for discrete linear
Hamiltonian systems. ... Stability criteria for linear periodic Hamiltonian systems. J. Math.
Anal. Appl. 367, 329–336 (2010)
[15] XH Tang, M Zhang, Lyapunov inequalities and stability for linear Hamil-
tonian systems. J. Diff....
...
Examples of Linear and Nonlinear Systems
Table 5-1 provides examples of common linear and nonlinear systems. As you
go through the lists, keep in mind the mathematician's view of linearity
(homogeneity, ... change.
Fourier
Decomposition
x[n]
x
C1
[n]
x
C2
[n]
x
C8
[n]
x
S1
[n]
x
S2
[n]
x
S8
[n]
x
C0
[n]
x
S0
[n]
x
C3
[n]
x
S3
[n]
cosine waves
sine waves
Chapter 5- LinearSystems 95
Table 5-1
Examples of linear and nonlinear systems. Formally, linearsystems are defined by the properties
of homogeneity, ...
Alternatives to Linearity
To appreciate the importance of linear systems, consider that there is only one
major strategy for analyzing systems that are nonlinear. That strategy is to
make the nonlinear...
... for conventional MIMO systems has been extensively studied in
various scenarios in the past decade [23–26].
1.1.3 AF MIMO Relay Systems
The benefits of multiple-antenna systems can be directly ... Relay Sys-
tems: In this chapter, joint design of linear relay precoder and destination
equalizer for dual-hop non-regenerative AF MIMO-OFDM systems under
channel estimation errors is investigated. ... of the more complicated AF MIMO relay
systems.
Capacity bounds under different channel state information (CSI) assumptions
for single-user AF MIMO relay systems have been derived in [27], [28]....
... the arithmetic mean.
Section I. Solving LinearSystems 3
works. The next example introduces that algorithm, called Gauss’ method (or
Gaussian elimination or linear elimination). It transforms the ... safe in that it never loses solutions or picks up extraneous solutions.
32 Chapter One. Linear Systems
II Linear Geometry of n-Space
For readers who have seen the elements of vectors before, in ... k
1.21 This system is not linear, in some sense,
2 sin α − cos β + 3 tan γ = 3
4 sin α + 2 cos β − 2 tan γ = 10
6 sin α − 3 cos β + tan γ = 9
50 Chapter One. Linear Systems
We think of these...
... endpoints k
1
, ,k
2s
∈{0, 1, ,N}; this
Annals of Mathematics
Isomonodromy
transformations of linear
systems of difference
equations
By Alexei Borodin
ISOMONODROMY TRANSFORMATIONS
1147
probability ... closed path γ in C avoiding the singular points {x
k
} then
the columns of Y will change into their linear combinations: Y →YM
γ
. Here
M
γ
is a constant invertible matrix which depends only on the ... class
of γ. It is called the monodromy matrix corresponding to γ. The monodromy
matrices define a linear representation of the fundamental group of C with
n punctures. The basic isomonodromy problem...
... method to construct a well-posed linear system is to use one
or several well-posed linearsystems to construct a new one. The following
40 Well-posed linear systems
The easy proof of this lemma ... Actually, the splitting of A&B
46 Well-posed linear systems
2.3 Basic examples of well-posed linear systems
Our first example of a well-posed linear system is the one discussed in Section
2.1:
Proposition ... of various notions
known from the theory of finite-dimensional systems to the setting of L
p
-
well-posed linear systems, and even to systems generated by arbitrary system
nodes. Some of the extensions...
... in
Three
Unknowns
44
7 Systems of
Linear
Inequalities in Any
Number
of
Unknowns
52
8.
The
Solution
of a System of
Linear
Inequalities
'by
Successive
Reduction of
the
Number
of
Unknowns
57
9.
Incompatible
Systems ... to
carry
out
the
analysis of these systems from
.general positions, i.e. so
that
the
results
obtained
may
be easily
extended to systems in a larger
number
of
unknowns.
The
solution
of
any
system of linear inequalities ... inequalities is in
the
long
run
reduced to
the
solution
of a number
of
systems
of
linear equations.
We shall
regard
the
solution
of a system of linear
equations
as
something
simple, as an
elementary
operation,
and
shall
not
be
I...