Graph-Grammars and Their Application to Computer Science: 3rd International Workshop Warrenton, Virginia, USA, December 2–6, 1986

616 Pages·1987·11.786 MB·English

by  Hartmut Ehrig (auth.), Hartmut Ehrig, Manfred Nagl, Grzegorz Rozenberg, Azriel Rosenfeld (eds.)

Lecture Notes ni
Computer Science
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Editors
Hartmut Ehrig
Fachbereich 20, Informatik, Technische Universitfit Berlin
Franklinstra6e 28/29, 1000 Berlin 10, Federal Republic of Germany
Manfred Nagl
Lehrstuhl fur Informatik ,111 RWTH Aachen
AhornstraBe 55, 5100 Aachen, Federal Republic of Germany
Grzegorz Rozenberg
Institute of Applied Mathematics and Computer Science
University of Leiden
P.O. Box 9512, 2300 Leiden, The Netherlands
Azriel Rosenfeld
Center for Automation Research, University of Maryland
College Park, MD 20742-3411, USA
CR Subject Classification (1987): E.1, D.2, D.3, F.1, E2, F.4, 5.1
ISBN 3-540-18771-5 Springer-Verlag Berlin Heidelberg New York
ISBN 0-387-18771-5 Springer-Verlag New York Berlin Heidelberg
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Preface
The generic term "graph-grammars" refers to a variety of methods
for specifying (possibly infinite) sets of graphs or sets of maps. The
area of graph-grammars has originated in the late 60s motivated by
considerations concerning pattern recognition - since then the list of
areas which have interacted with the development of graph-grammars has
grown quite impressively. It includes pattern recognition, software
specification and development, VLSI layout schemes, data bases,
A-calculus, analysis of concurrent systems, massively parallel computer
architectures, incremental compilers, computer animation, complexity
theory, developmental biology, music composition, representation of
physical solids, and many many others.
Through the last 20 years the study of graph-grammars has
developed at a steady pace into an active research field holding the
interest of many researchers of quite different backgrounds from all
over the world.
This continuing interest has led to three international workshops
on graph-grammars and their applications. The first two were held in
Bad Honnef and in Osnabruck (Federal Republic of Germany) in 1978 and
1982. The third workshop took place in December 1986 in Warrenton,
Virginia, U.S.A.
This volume is based on the contributions presented in Warrenton -
not all of the papers presented at the meeting appear in this volume
and also some papers from this volume were not presented at the
workshop. We felt that in this way the field would be better
represented.
The volume consists of two parts: Part I presents tutorial
introductions to a number of basic graph and map rewriting mechanisms.
Part II contains technical contributions. We hope that this collection
of papers will provide the reader with an up-to-date overview of
current trends in graph-grammars. In particular we hope that the volume
will help the "uninitiated" reader to join this fascinating area which
on the one hand offers many challenging mathematical problems while on
the other hand provides a whole spectrum of potential applications.
We are grateful to NSF for financially supporting the workshop and
we are very indebted to about 60 participants of the workshop for
creating such a scientifically stimulating and socially pleasant week.
H. Ehrig, M. Nagl, A. Rosenfeld, G. Rozenberg
Table of Contents
PART :I Tutorial Introductions
Tutorial introduction to the algebraic approach of graph-grammars
H. Ehrig
May we introduce to you: hyperedge replacement
A. Habel and H.-J. Kreowski 15
An introduction to parallel map generating systems
A. Lindenmayer 27
Set theoretic approaches to graph-grammars
M. Nagl 41
An introduction to the NLC way of rewriting graphs
G. Rozenberg 55
Array grammars
A. Rosenfeld 67
PART :II Technical Contributions
Graph grammar based specification of interconnection structures for
massively parallel computation
D.A. Bailey and J.E. Cuny 73
Towards distributed graph-grammars
.P Boehm, H. Ehrig, U. Hummert, and M. L6we 86
On partially ordered graph-grammars
F.J. Brandenburg 99
A representation of graphs by algebraic expressions and its use for
graph rewriting systems
B. Courcelle 112
On context-free sets of graphs and their monadic second-order theory
.B Courcelle 133
IV
Restricting the complexity of regular DNLC languages
IJ.J. Aalbersberg, .J Engelfriet, and G. Rozenberg 147
Apex graph-grammars
J. Engelfriet, G. Leih, and G. Rozenberg 167
Graph-grammar engineering: A software specification method
G. Engels, C. Lewerentz, and W. Sch~fer 186
A linguistic formalism for engineering solid modeling
P. Fitzhorn 202
Graph-grammars and diagram editing
H. G6ttler 216
Graphics and their grammars
.L Hess and B.H. Mayoh 232
On network algebras and recursive equations
G. Hotz, R. Kolla, and P. Molitor 250
ADA-concurrency specified by graph grammars
M. Jackel 262
Basic notions of actor grammars: A graph grammar model for actor
computation
D. Janssens and G. Rozenberg 280
Embedding rule independent theory of graph grammars
.J Jeffs 299
Supporting the software development process with attributed NLC graph
grammars
S.M. Kaplan, S.K. Goering, and R.H. Campbell 309
Practical applications of precedence graph grammars
M. Kaul 326
Is parallelism already concurrency? Part :I Derivations in graph
grammars
H.-J. Kreowski 343
VII
Is parallelism already concurrency? Part 2: Non sequential
processes in graph grammars
H.-J. Kreowski and A. Wilharm 361
Map OL-systems with edge label control: Comparison of marker and
cyclic systems
M.J.M. de Boer and A. Lindenmayer 378
From OL and IL map systems to indeterminate and determinate growth
in plant morphogenesis
J. L~ck and H.B. LUck 393
Fundamentals of edge-label controlled graph grammars
M.G. Main and G. Rozenberg 411
Parallelism analysis in rule-based systems using graph grammars
D. Moldovan and .F Parisi-Presicce 427
An efficient algorithm for the solution of hierarchical networks of
contraints
U. Montanari and .F Rossi 440
A software development environment based on graph technology
M. Nagl 458
Map OL systems with markers
A. Nakamura, A. Lindenmayer, and .K Aizawa 479
Graph rewriting with unification and composition
.F Parisi-Presicce, H. Ehrig, and U. Montanari 496
Complexity of pattern generation via planar parallel binary
fission/fusion grammars
J.W. Carlyle, S.A. Greibach, and A. Paz 515
Applications of L-systems to computer imagery
P. Prusinkiewicz 534
Advances in array languages
R. Siromoney 549
IJIV
Rosenfeld's cycle grammars and kolam
G. Siromoney and R. Siromoney 564
Application of graph grammars in music composing systems
F. Wankm~ller 580
Boundary NLC and partition controlled graph grammars
E. Welzl 593
PART I
TUTORIAL INTRODUCTIONS

TUTORIAL INTRODUCTION TO THE ALGEBRAIC
APPROACH OF GRAPH GRAMMARS
Hartmut Ehrig
Technical University Berlin
April, 1987
ABSTRACT: This tutorial introduction is intended to provide an intuitive understanding of
the general format of the graph grammar mechanism underlying the algebraic approach.
We point out the essential role of the gluing construction and discuss basic constructions
in connection with sequential and parallel independence of derivations and what to do in
the case of sequential resp. parallel dependence.
1. GENERAL FORMAT OF PRODUCTIONS AND DIRECT DERIVATIONS
1.1 Productions
A production ;Si a paiir of graphs (B1,B2), called left and right hand side respectively, to-
gether with designated gluing points K1 of 1B and K2 of B2 which are in bijective
correspondence to each other.
1.2 Direct Derivations
A direct derivation from a mother graph G to a daughter graph H is obtained in three
steps:
Step 1: Match the left hand side 1B of the production with a subgraph of the
mother graph G and check the gluing condition (see 1.3).
Step 2: Consider the left hand side 1B except of its gluing points K1, i.e. B1-K1,
and remove it from the mother graph G. The result is a context graph D
which still contains the gluing points K1.
Step 3: Add the right hand side B2 to the context graph D by gluing together the
gluing points K1 of D with corresponding gluing points K2 of B2. The
result is the daughter graph H.
1.3 Gluing Condition
The boundary points BOUNDARY are those points in 1B (considered as subgraph of G)
which are source or target of arcs in G-B1. The gluing points GLUING of 1B are given
by KI. The condition
BOUNDARY ---~ GLUING
is called gluing condition and assures that the context D in step 2 is indeed a graph.
2. EXAMPLE ("Santa Claus going to White House")
This example was presented at the workshop (near to the White House) on December 6.
The production shows how a Santa Claus cap is replaced by a silk hat. The mother graph
G is Santa Claus with his original cap and the daughter graph H Santa Claus with silk hat.
eehT production and the graphs G and H are given in 2.1 and 2.2 below: