Table Of ContentLecture Notes ni
Computer Science
Edited by .G Goos and .J Hartmanis
26
,atamotuA
segaugnaL dna gnimmargorP
Colloquium, Fifth Udine, Italy, July 1978 17-21,
Edited by .G Ausiello and .C B0hm
I
galreV-regnirpS
Berlin Heidelberq NewYork 1978
Editorial Board
.P Brinch Hansen .D Gries C. Moler G. SeegmQller
.J Stoer .N Wirth
Editors
Giorgio AusieHo
C.S.S.C.C.A.-C.N.R.
lstituto di Automatica
Via Eudossiana 81
Roma 00184/Italy
Corrado BShm
Istituto Matematico
,,Guido Castelnuovo"
Universit& di Roma
Piazzale delle Scienze
Roma 00100/Italy
Classifications AMS Subject :)0791( 68-XX
RC Classifications Subject :)4791( ,1.4 5.3 5.2, 4.2,
3-540-08860-1 tSBN galreV-regnirpS Berlin NewYork Heidelberg
NBSJ 0-387-08860-t galreV-regnirpS Heidelberg NewYork Berlin
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agreement with the publisher.
© by Springer-Vertag Berlin Heidelberg 1978
Printed in Germany
Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr.
2145/3140-543210
PREFACE
The Fifth International Colloquium on Automata, Languages and Programming
(I.C.A.L.P.) was preceded by similar colloquia in Paris (1972), Saar-
bracken (1974; see LNCS vol. 14), Edinburgh (1976), Turku (1977; see
LNCS vol. 52). This series of conferences is sponsored by the European
Association for Theoretical Computer Science, and is to be held each
year (starting in 1976) in a different European country. The series of
conferences will be published in the Lecture Notes in Computer Science.
In addition to the main topics treated - automata theory, formal lan-
guages and theory of programming - other areas such as computational
complexity and l-calculus are also represented in the present volume.
The papers contained in this volume and presented at Fifth I.C.A.L.P. in
Udine (Italy) from July 17 to 21, 1978 were selected among over 90 sub-
mitted papers. The Program Committee, consisted of G. Ausiello, C. B6hm,
H. Barendregt, R. Burstall, J.W. De Bakker, G. Degli Antoni, E. Engeler,
J. Hartmanis, I.M. Havel, J. Loeckx, U. Montanari, M. Nivat, M. Paterson,
A. Paz, J.F. Perrot. The editors feel very grateful to the other members
of the Program Committee and to all referees that helped the Program
Committee in evaluating the submitted papers. In particular we like to
thank: L. Aiello, H. Alt, K. Apt, G. Barth, J. Be~va~, J. Berstel,
A. Bertoni, D.P. Borer, A. Celentano, G. Ci0ffi, R. Cohen, .S Crespi
Reghizzi, J. Darlington, A. de Bruin, P.P.Degano, G. De Michelis, S. Even,
G. Germano, J.A. Goguen, M.J.C. Gordon, P. Greussay, J. Gruska, A. Itai,
.R Kemp, J. Kr~l, I. Kramosil, G. Levi, M. Lucertini, A. Martelli,
G. Mauri, D.B. McQueen, K. Mehlhorn, L.G.L.T. Merteens, P. Miglioli,
R. Milner, C. Montangero, A. Nijholt, D. Park, G.D. Plotkin, B. Robinet,
E. Rosenschein, E. Rosinger, B. Rovan, C.P. Schnorr, J. Schwarz, M.B.Smith,
S. Termini, F. Turini, D. Turner, L.C. Valiant, P. van Emde Boas, J. van
Lamsveerde, J. van Leeuwen, P.M.B. Vitanyi, W.W. Wadge, C. Wadsworth,
C. Whitby-Strevens, P. Yoeli.
Finally we would like to express our gratitude to the Italian National
Research Council for providing their financial support to the Fifth
I.C.A.L.P. and the Centro di Studio dei Sistemi di Controllo e Calcolo
Automatici (C.S.S.C.C.A.-C.N.R., Rome), the Centro Internazionale di
Scienze Meccaniche (C.I.S.M., Udine), the Istituto di Automatica of the
University of Rome that took the charge of the organization of the Con-
ference.
G. Ausiello C. B~hm Rome, May 1978
C O N T E N T S
J. Albert, H. Maurer, G. Rozenberg
Simple EOL forms under uniform interpretation
generating CF languages ....................................
D. Altenkamp, K. Mehlhorn
Codes: unequal probabilities unequal letter costs .......... 15
A. Arnold, M. Dauchet
Sur l'inversion des morphismes d'arbres .................... 26
G. Barth
Grammars with dynamic control sets ........ . ................. 36
J. Beauquier
Ambiguit~ forte ............................................ 52
P. Berman
Relationship betweendensity and deterministic
complexity of NP-complete languages ........................ 63
G. Berry
Stable models of typed l-Calculi ........................... 72
J. Biskup
Path ~easures of Turing Machines computations .............. 90
J.M. Boe
Une famille remarquable de codes ind~composables ........... 105
R.V. Book, S. Greibach, C. Wrathall
Comparisons and reset machines ............................. 113
B. Commentz-Walter
Size-depth tradeoff in boolean formulas .................... 125
IV
M. Coppo~ M. Dezani-Ciancaglini, S. Ronchi
(Semi)-separability of finite sets of terms in
Scott's D -models of the l-calculus ........................ 142
A.B~ Cremers, ToN. Hibbard
Mutual exclusion of N processors using an 0 (N)-valued
message variable ........................................... 165
W. Dammt E. Fehr
On the power of self-application and higher
type recursion ............. . ............................... 177
D. Dobkin, I. Munro
Time and space bounds for selection problems ............... 192
H. Ehrig, H.J. Kreowskif P. Padawitz
Stepwise specification and implementation
of abstract data types ..................................... 205
S. Fortune~ J. Hopcroft, E.M. Schmidt
The complexity of equivalence and containment
for free single variable program schemes ................... 227
Z. Galil
On improving the worst case running time of the
Boyer-Moore string matching algorithm ...................... 241
J. Gallier
Semantics and correctness of nondeterministic
flowchart programs with recursive procedures .............. 251
D. Harel
Arithmetical completeness in logics of programs ............ 268
Ao Itai~ M. Rodeh
Covering a graph by circuits ............................... 289
Vii
A. Lingas
A p-space complete problem related to a pebble game ........ 300
M. Mignotte
Some effective results about linear recursive sequences .... 322
A. Nijholt
On the parsing and covering of simple chain grammars ....... 330
J.E. Pin
Sur un cas particulier de la conjecture de Cerny ........... 345
J.K. Price, D° Wotschke
States can sometimes do more than stack symbols
in PDA's ................................................... 353
A. Restivo
Some decision results for recognizable sets
in arbitrary monoids ....................................... 363
C. Reutenauer
Sur les s~ries rationnelles en variables
non commutatives ........................................... 372
M. Saarinen
On constructing efficient evaluators for attribute
grammars ................................................... 382
P. Sall~
Une extension de la th~orie des types en l-calcul ........... 398
W. Savitch
Parallel and nondeterministic time complexity classes ...... 411
C.P. Schnorr
Multiterminal network flow and connectivity
in unsymmetrical networks .................................. 425
Vlll
E. Scioreu A. Tang
Admissible coherent c.p.o.~s ............................... 440
T. Toffo!i
Integration of the phase-difference relations in
asynchronous, sequential networks .......................... 457
R. Valk
Self-modifying nets~ a natural extension of Petri nets ..... 464
M. Venturini Zilli
Head recurrent terms in combinatory logic:
A generalization of the notion of head normal form ......... 477
R. Wiehagen
Characterization problems in the theory
of inductive inference ..................................... 494
SIMPLE EOL FORMS UNDER UNIFORM
INTERPRETATION GENERATING CF LANGUAGES
J~rgen Albert )1 , Hermann Maurer )2 , Grzegorz Rozenberg )3
1)University of Karlsruhe, W-Germany
2)Technische Universitaet Graz, Austria
3)University of Antwerp, Belgium
Abstract. In this paper we consider simple EOL forms (forms with a
single terminal and single nonterminal) under uniform interpretations.
We present a contribution to the analysis of generative power of simple
EOL forms by establishing easily decidable necessary and sufficient
conditions for simple EOL forms to generate (under uniform interpre-
tations) CF languages only.
.I Introduction
The systematic study of grammatical similarity was begun in the
pioneering paper ]2[ and extended to L-s~stems in [7]. The central
concept introduced in [7] is the notion of an EOL form and its inter~
pretations: each EOL system F - if understood as EOL form - generates,
via the interpretation mechanism, a family of structurally related
languages. Variations of the basic interpretation mechanism are
possible, with the so-called uniform interpretation as one of the
most promising candidates [8].
One of the central problems of EOL form theory is the systematic
examination of language families generated by EOL forms and the study
of generative capacity of EOL forms. Consequently, much effort has
been concentrated on this type of problem and significant insights
have been obtained. Fundamental results concerning generative capa-
city have already been established in ]7[ and ideas introduced there
have been pursued in more detail in later papers. In particular, the
notion of a complete form a( form generating all EOL languages) has
been thoroughly investigated for simple forms (forms with a single
terminal and single nonterminal) in [3]; the notion of goodness
a( property involving subfamilies of families generated by EOL forms)
has been further pursued in [10] and [11]; the class of CF languages
cannot be generated by EOL forms under (ordinary) interpretation
according to [I]; and [12] takes a new approach to the study of
language classes generated by EeL forms by introducing the notion of
generators° The generative capacity of non EeL L forms is the central
topic of the papers [9], [13], [16], [4] and [6]. In contrast to the
large nu~er of papers quoted dealing with topics suggested in [7] ,
the notion of uniform interpretation, also proposed in [7] has received
little attention sofar beyond [8]. We believe that a further study of
uniformi nterpretations is essential and will increase the understanding
of both L forms and L systems.
This paper is to be seen as a first but crucial step in t~is direction.
We present a complete classification of all simple EeL forms which
under uniform interpretation yield CF languages only, yield at least
one non-CF-language, respectively. This classification result, as
expressed in our main Theorem 4 in Section 3, shows that some sur-
prisingly complicated EeL fQ!ms generate under uniform interpretation
nothing but CF languages, while other surprisingly trivial EeL forms
(such as the forms with productionsS+a, S+SS, a÷a, a÷e or just S+a, S+S,
a+s, a÷aS) generate, even under uniform interpretation,non-CF-languages.
The rest of this paper is structured as follows. The next section 2
reviews definitions concerning L systems and L forms. Section 3 con-
tains the results. Theorems 1,2,3 are of modest interest in themselves
(and thus stated as theorems rather than lemmat~). They lead to the
central classification theorem, Theorem 4, whose proof constitutes the
remainder of the paper. The table, presented in this proof, of the
38 possible types of minimal EOL forms yielding non-CF-languages should
be of independent interest for further investigations of uniform inter-
pretations of EeL forms.
2. Definitions
In this section some basic definitions concerning EeL forms and their
interpretations are reviewed. An EeL system G is a quadruple
G=(V,E,P,S), where V is a finite set of symbols, the alphabet of G,
c I V is called the set of terminals, V - Z is the set of nonterminals,
P is a finite set of pairs (e,x) with ~6V, x6V ~ and for each ~6V there
is at least one such pair in P. The elements (~,x) of P are called
productions or rules and are usually written as ~÷x. S is an element
of V-Z and is called the startsymbol.
Forwords X=ela2...en, ~i6V and
y=ylY2...yn ~ Yi£V ~, we write X~y if ei÷Yi is in P for every i.
o m
We write x~x for every x6V* and x~y for some m_> I if there is a
m-1
z6V* such that x~z~y.
By x~y we mean x~y n for some n_>0, and x~y + stands for x~y n for
some . 1 > n
The language generated by G is denoted by L(G) and defined by
L(G) = {X6Z*[S~x}.
The family of all EOL languages is denoted by ~OL' i.e. ~EOL={L(G) IG
is an EOL system}. Similarly, we denote by ~FIN' ~REG' ~LIN and
~CF the classes of finite, regular, linear and context-free languages,
respectively. We now review the notion of an EOL form F and its inter-
pretations as introduced in [7] for the definition of structurally
related EOL systems.
An EOL form F is an EOL system F=(V,E,P,S). An EOL system F'=(V',E',P',S')
is called an interpretation of F (modulo ~), symbolically F'4F(u) if
is a substitution defined on V and )i( - )v( hold:
)i( ~(A) c_ V'-E' for each A6V-Z,
(ii) ~(a) c_ S' for each a6Z,
(iii)~(a)D~(~)=~ for all ~,~ in V, ~#~,
(iv) P' c ~(p) where
(P)={B+Yla+x6P,B6~(a), y6u(x) }
)v( S' is in D(S).
The family of EOL forms generated by F is defined by ~(F)={F'IF'~F}
and the family of languages generated by F is ~(F)={L(F') IF'~F}.
An important modification of this type of interpretation, first
introduced in [8] , is called uniform interpretation and defined as
follows. F' is a uniform interpretation of F, in symbols F'~ F, if
u
F'~F and in (iv) even P' ~u(P) holds, where
~u(P)={~o'+~ 'I .... ~t'6~(P) i~o+~1...~t6P,~i'£~(ai), and ~r=as6S
implies ~ ,=~ },
r s
Thus, the interpretation has to be uniform on terminals. In analogy to
the above definitions we introduce ~u(F) = {F'IF'~uF} and
Zu(F) :={L(F') IF'~uF}.
For a word x we use alph(x) to denote the set of all symbols occuring
in x and for a language M we generalize this notion by
alph )M( = ~--] alph )x( .
x6M
Given some finite set Z, card )Z( is the number of elements contained
