Graph Transformations in Computer Science: International Workshop Dagstuhl Castle, Germany, January 4–8, 1993 Proceedings

404 Pages·1994·7.25 MB·English

by  Kunio Aizawa

Lecture Notes in Computer Science 776
Edited by .G Goos and .J Hartmanis
Advisory Board: .W Brauer .D Gries .J Stoer
Hans Jtirgen Schneider Hartmut ).sdE(girhE
hparG snoitamrofsnarT
ni retupmoC Science
International pohskroW
Dagstuhl Castle, Germany, January 4-8, 3991
sgnideecorP
galreV-regnirpS
Berlin Heidelberg NewYork
London Paris Tokyo
Hong Kong Barcelona
tsepaduB
Series Editors
Gerhard Goos Juris Hartmanis
Universit~it Karlsruhe Comell University
Postfach 69 80 Department of Computer Science
Vincenz-Priessnitz-Stra6e l 4130 Upson Hall
D-76131 Karlsruhe, Germany Ithaca, NY 14853, USA
Volume Editors
Hans Jiirgen Schneider
Lehrstuhl ftir Programmiersprachen, Universit~it Erlangen-Ntirnberg
Martensstral3e 3, D-91058 Erlangen, Germany
Hartmut Ehrig
Institut ftir Software und Theoretische Informatik, Technische Universit~it Berlin
FranklinstraBe 28/29, D-10587 Berlin, Germany
CR Subject Classification (1991): G.2.2, E4.2, D.2.2, E.1, 1.3.5
ISBN 3-540-57787-4 Springer-Verlag Berlin Heidelberg New York
ISBN 0-387-57787-4 Springer-Verlag New York Berlin Heidelberg
CIP data applied for
This work is subject to copyright. All rights are reserved, whether the whole or part
of the material is concerned, specifically the rights of translation, reprinting, re-use
of illustrations, recitation, broadcasting, reproduction on microfilms or in any other
way, and storage in data banks. Duplication of this publication or parts thereof is
permitted only under the provisions of the German Copyright Law of September 9,
1965, in its current version, and permission for use must always be obtained from
Springer-Verlag. Violations are liable for prosecution under the German Copyright
Law.
(cid:14)9 Springer-Verlag Berlin Heidelberg 1994
Printed in Germany
Typesetting: Camera-ready by author
SPIN: 10131942 45/3140-543210 - Printed on acid-free paper
Preface
The research area of graph grammars and graph transformations is a relatively young disci-
pline of computer science. Its origins date back to the early 1970s. Nevertheless methods,
techniques, and results from the area of graph transformation have already been studied and
applied in many fields of computer science such as formal language theory, pattern recogni-
tion and generation, compiler construction, software engineering, concurrent and distributed
systems modelling, database design and theory, and so on.
This wide applicability is due to the fact that graphs are a very natural way to explain
complex situations on an intuitive level. Hence they are used in computer science almost
everywhere, e.g., as data- and control flow diagrams, entity relationship diagrams, Petri nets,
visualization of soft- and hardware architectures, evolution diagrams of non-deterministic
processes, SADT diagrams, and many more. Like the '!token game" for Petri nets, graph
transformation brings dynamics to all these descriptions, since it can describe the evolution of
graphical structures. Therefore graph transformation becomes attractive as a "programming
paradigm" for complex structured software and graphical interfaces. In particular graph
rewriting is promising as a comprehensive framework in which the transformation of all
these very different structures can be modelled and studied in a uniform way.
This Dagstuhl Seminar was prepared by a program committee consisting of
Bruno Courcell e (Bordeaux)
Hartmut Ehrig (Berlin)
Grzegorz Rozenberg (Leiden)
Hans Jfirgen Schneider (Erlangen)
During the seminar 33 lectures and 3 system demonstrations where presented by the parti-
cipants from 8 European countries, U.S.A. and Japan in the following areas:
Foundations of graph grammars and transformations
-
- Applications of graph transformations to
(cid:12)9 Concurrent computing
(cid:12)9 Specification and programming
(cid:12)9 Pattern generation and recognition
The system demonstrations in the evening showed efficient implementations of the algebraic
approach to graph transformations (AGG-System), of a software specification language based
on graph rewriting (PROGRESS) and of a functional programming language (Concurrent
Clean) based on term graph rewriting. In each case the theoretical techniques of the under-
lying approach and typical applications were demonstrated in corresponding lectures during
the day. In addition, interesting new applications of graph transformations were presented
in several lectures in the following areas: concurrent constraint programming; actor systems;
specification of languages for distributed systems, of hybrid database languages, and of an
efficient narrowing machine; and - last but not least - pretty pattern generation and recog-
nition ranging from graphical modelling for CAD to abstractions of modern art including
Escher and Picasso.
In the lectures concerning foundations, on one hand new results concerning graph languages
and graph automata and their connections to decision problems were presented. On the
other hand new concepts and results for the algebraic approach to graph transformations
IV
based on double and single pushouts were shown. Notions for abstraction and semantical
constructions were given leading to canonical derivation sequences, true concurrency and
event structures, and also extensions of results from graph grammars to HLR (High Level
Replacement) systems. The HLR approach is a categorical unification of different approaches
with several interesting new applications including those to rule based modular system design
and transformation and refinement of Petri nets.
Altogether it was a very fruitful interaction between theory, applications, and practical
demonstrations.
At the end of the seminar, we invited the participants to submit final versions of their papers
to a regular refereeing process. We wish to thank all the people who served as referees -
and have done a good job and spent a lot of time - for conscientiously reading preliminary
and final versions. Especially, we would like to express our warmest thanks to the members
of the Program Committee and in particular to Ugo Montanari, who additionally joined us
and took over some part of handling the refereeing process. After all, we could accept only
24 papers for publication in these proceedings.
Last but not least, we owe thanks to Springer-Verlag for producing this volume in the usual
outstanding quality.
January 1994 Hartmut Ehrig
Hans Jfirgen Schneider
Contents
Path-Controlled Graph Grammars for Multiresolution Image Processing
and Analysis
K. Aizawa/A. Nakamura ............................................................... 1
Syntax and Semantics of Hybrid Database Languages
M. Andries/G. Engels ................................................................ 91
Decomposability Helps for Deciding Logics of Knowledge and Belief
S. Arnborg ........................................................................... 73
Extending Graph Rewriting with Copying
E. Barendsen/S. Smetsers ............................................................ 15
Graph-Grammar Semantics of a Higher-Order Programming Language for
Distributed Systems
K. Barthelmann/G. Schied ........................................................... 17
Abstract Graph Derivations in the Double Pushout Approach
A. Corradini/H. Ehrig/M. LSwe/U. Montanari/F. Rossi .............................. 68
Note on Standard Representation of Graphs and Graph Derivations
A. Corradini/H. Ehrig/M. LSwe/U. Montanari/F. Rossi ............................. 401
Jungle Rewriting: an Abstract Description of a Lazy Narrowing Machine
A. Corradini/D. Wolz ............................................................... 911
Recognizable Sets of Graphs of Bounded Tree-Width
B. Courcelle/J. Lagergren ........................................................... 831
Canonical Derivations for High-Level Replacement Systems
H. Ehrig/H.-J. Kreowski/G. Taentzer ................................................ 351
A Computational Model for Generic Graph Functions
M. Gemis/J. Paredaens/P. Peelman/J. Van den Bussche ............................. 071
Graphs and Designing
E. Grabska .......................................................................... 881
ESM Systems and the Composition of Their Computations
D. Janssens ......................................................................... 302
Relational Structures and Their Partial Morphisms in View of Single
Pushout Rewriting
Y. Kawahara/Y. Mizoguchi .......................................................... 812
Single Pushout Transformations of Equationally Defined Graph Structures with
Applications to Actor Systems
M. Iiorff ............................................................................ 432
Parallelism in Single-Pushout Graph Rewriting
M. Lb'we/J. Dingel .................................................................. 842
Semantics of Full Statecharts Based on Graph Rewriting
A. Maggiolo-Schettini/A. Peron ..................................................... 562
VIII
Contextual Occurrence Nets and Concurrent Constraint Programming
U. Montanari/F. Rossi .............................................................. 082
Uniform-Modelling ni Graph Grammar Specifications
M. Nagl ............................................................................. 692
Set-Theoretic Graph Rewriting
J.-C. Rrloult/F. I"oisin .............................................................. 213
On Relating Rewriting Systems and Graph Grammars to Evcnt Structures
G, Schied ........................................................................... 623
Logic Based Structure Rewriting Systems
,4. Schiirr ........................................................................... 143
Guaranteeing Safe Destructive Updates Through a Type System with Uniqueness
Intormation for Graphs
S. Smetsers/E. Barendsen/M. v. Eekelen/R. Plasmeijer .............................. 853
Amalgamated Graph Transformations and Their esU for Specifying AGG -
an Algebraic Graph Grammar System
G. Taentzer/M. Beyer ............................................................... 083
List of authors ...................................................................... 593
dellortnoC-htaP hparG srammarG
rof
noituloseritluM egamI gnissecorP dna Analysis
Kunio Aizawa 1 and Akira Nakamura 2
1 tnemtrapeD of Applied scitamehtaM
Hiroshima University
Higashi-Hiroshima, 724 Japan
tnemtrapeD2 of Computer Science
Meiji University
Kawasaki, Kanagawa, 214 Japan
Abstract: In this paper, we define graph compression rules for the graphs
representing two-dimensional rectangular grids with black and white pixels by making use
of the PCE way of embedding. The compression rules rewrite four nodes having same
label and forming a square into a node with the label. It also inserts and deletes nodes with
special labels to preserve the neighborhood relations in the original image. Then we
introduce an image compression algorithm using the concept of our graph compression
rules. We show that the time complexity of our algorithm is O(Nlog2N), where N is the
number of the black nodes of input graph, which is same as the case of the best quadtree
.noitatneserper
Keywords: graph grammars, path-controlled embedding, qurdtrees, normalized
quadtrees, region representation
STNETNOC
.1 Introduction
2. Basic snoitinifed
3. Image compression rules on graphs
4. Optimal compression mhtirogla
5. Conclusions
.1 Introduction
The graph structure is a strong formalism for representing pictures in syntactic pattern
recognition. Many models for graph grammars have been proposed as a kind of hyper-
dimensional generating systems (see e.g., 1, 2, and 3), whereas the use of such
grammars for pattern recognition is relatively infrequent. As one of such graph grammars,
we introduced node-replacement path-controlled embedding graph grammars (nPCE graph
grammars) in 4 for describing uniform structures. Originally, such embedding
mechanism using paths of edges was introduced in 5 and 6. These works are collected
in 7. Our grammars utilize partial path groups to def'me their embedding function.
On the other hand, region representation on digital spaces is an important issue in image
processing and computer graphics. The quadtree representation of a digital image provides
a variable resolution encoding of a region according to the sizes and number of maximal
nonoverlapping blocks. It also provides easy computation for topological relations such as
adjacency, connectedness, and borders. Samet 8, 9 provide good tutorial and
bibliography of the researches on quadtrees as well as their applications. Recently, in 10,
quadtree representation are used as a data structures for parallel image recognition.
In this paper, we define graph compression rules for the graphs representing two-
dimensional rectangular grids with black and white pixels by making use of the PCE way
of embedding. We refer to the subset of black pixels as the "region" and to the subset of
white pixels as the "region's background." The compression rules rewrite four nodes
having same label and forming a square into a node with the label. It also inserts and
deletes nodes with special labels to preserve the neighborhood relations in the original
image. Then we introduce an image compression algorithm using the concept of our graph
compression rules. We show that the time complexity of our algorithm is O(Nlog2N),
where N is the number of the black nodes of input graph, which is same as the case of the
best quadtree representation.
2. Basic definitions
In this section, we review the definitions of the string descriptions of graphs 11 and
nPCE graph grammars 12.
Definition 2.1. A detcerid -edon dna dellebal-egde hparg )hparg-GDE( over Z and
F is a quintuple H = <V, E, Z, F, ,>~q where V is the finite, nonempty set of nodes, E is
the finite, nonempty set of node labels, F is the finite nonempty set of edge labels, E is the
set of edges of the form <v, k, w>, where u, we V, ~e F, :0q Z~---V is the node labelling
function.
Let us take a set of edge labels as shown in Fig. 1 representing "EAST", "WEST,',
"NORTH", and "SOUTH", and ordered -h < -v < h < v.
%
x %% ~ V s,st, SS
h' %%%1,'" h
%Is -P
S S %%
S S %%
S S V t %%
s
.giF .1 ehT tes of edge .slebal
Definition 2.2. An EDG-graph H is called an OS-graph if
(1) for each ~.~ F there exists an inverse edge label ~-1~ F,
(2) F is simply ordered by a relation <,
(3) for each vE V, if there exists <v, ,.~ w>~ E then there does not exist <v, ,f" z>
such that .~ = "/or <z, 6, v>~ E such that .~=1-~
Now we review the definitions of nPCE graph grammars. These definitions of nPCE
graph grammars are slightly different from the former version 4 since the definitions of
the path group are different. Then we examine their powers for generating OS-graphs. At
first we review the definitions of the path groups describing the square grid 13.
Definition 2.3. A discrete space is a finitely presented abelian path group F = (X/D),
where X has 2n generators s 1, s 2 ..... s n, S1-1, s2 -1 ..... nS -1, and D contains all
relations other than the commutativity (sisjsi-lsj'l= )1 and the inverse iterations (sisi-l=l).
The square grid is a discrete space described by a four generators Sl= (north), s2= (east),
sl-l= (south), s2-1= (west), and D=~.
Note that the path groups defined above can also be defined on a graph generated by a
graph grammar by regarding the edge labels of the generated graph as the generators.
Definition 2.4. For any given OS-graph H, its node P, and a string r~={ClC2...ci} of
its edge labels, P~ is realizable on H if and only if there exists a set of nodes {P0, P1 ....
, Pi} such that P0=P and <Pj, cj, Pj.1 > or <Pj-1, cj -1, Pj> is an edge ofH (l<j<i).
We review briefly the definition of nPCE grammars using abelian path groups to
control embedding mechanism.