Table Of ContentLecture Notes ni
Computer Science
Edited by .G Goos and .J sinamtraH
511
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Eighth Colloquium
Acre (Akko), Israel
July 13-17, 1891
Edited by .S Even and .O Kariv
galreV-regnirpS
nilreB Heidelberg NewYork 1891
Editorial Board
W. Brauer P. Brinch Hansen D. Gries C. Moter G. Seegm(JIler
.J Stoer N. Wirth
Editors
Shimon Even
Oded Kariv
Dept. of Computer Science
Technion-lsrael Institute of Technology
32000 Haifa, Israel
AMS Subject Classifications (1981): 68-XX
CR Subject Classifications (1974): 4.1, 4~2, 5.2, 5.3
ISBN 3-540-10843-2 Springer-Verlag Berlin Heidelberg New York
tSBN 0-387-10843-2 Springer-Vertag New York Heidelberg Berlin
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PREFACE
ICALP is the acronym of the annual international Colloquium on Automata,
Languages and Programming sponsored by the European Association for Theoretical
Computer Science (EATCS). It is a broad-based conference covering all aspects of
the foundations of computer science, including such topics as automata, formal
languages, analysis of algorithms, computational complexity, computability,
mathematical aspects of programming language definition, flow analysis, semantics
of programming languages, parsing, program verification, dynamic logic, rewriting
systems, cryptology, abstract data types, data structures and data base theory.
Previous ICALP conferences were held in Paris(!972), Saarbr~cken(1974), Edinburgh
(1976), Turku(1977), Udine(1978), Graz(!979) and Noordwijkerhout(1980).
SCALP 81 is the 8th conference of EATCS, covering once again a broad spectrum
of theoretic computer science. It is organized by the Computer Science Dept. of
the Technion and is to be held on July 13-17,1981, in Acre (Akko), Israel.
There are 44 papers in this volume, including 2 invited papers (by J.D. Ullman
and E. Bngeler). The other contributed papers were selected by a Selection Commi-
ttee (the names of its members are listed below) from 109 extended abstracts and
draft papers submitted in response to the call for papers. Each submitted paper
was sent for evaluation to three members of the Program Committee. The manuscripts,
however, were not formally refereed as several of them represent preliminary re-
ports of continuing research. It is anticipated that most of these documents will
appear in more polished and complete form in scientific journals.
The chairman of ICALP 81 and the organizing committee wish to thank all those
who submitted papers for consideration; members of the Program Committee (see be-
low) for their help in the evaluation of the papers, and the many who assisted in
this process (see next page); Maurice Nivat who was a host of the Selection Commi-
ttee meeting in Paris; all the institutions and corporations which support ICALP 81
(see list of supporters below); Mr. Henry Lochoff of "Eden-Tours" Ltd. for handling
the many touristic details related to the conference; Springer-Verlag for printing
this volume. Finally we wish to thank Ms. Anat Even and Ms. Belle Gologorsky and
the secretarial staff of the Computer Science Department of the Technion for their
assistance in all organizational matters related to the conference.
April 16, 1981 .S Even and O. Kariv
PROGRAM EETT149-~OC LOCAL ARRANGEMENTS
J.W. deBakker (Amsterdam)
Oded Kariv, Chairman
A. Blikle (Warsaw)
.C Boehm (Rome)
* S. Even (Haifa), Chairman
SUPPORTERS
* H.F. deGroote (Frankfurt)
I.M. 11avel (Prague)
Technion - Israel Institute of Technology
M.A. Harrison (Berkeley)
Israel Academy of Sciences and Humanities
R.M. Karp (Berkeley)
Israel National Council for Research and
.Z Manna (Stanford)
Development
H. Maurer (Graz)
RAFAEL - Armament Development Authority
.R Milner (Edinburgh)
I.B.M. Israel Ltd.
* M. Nivat (Paris)
Israel Discount Bank Ltd.
M. Paterson (Warwick)
EL-AL Israel Airlines
A. Paz (Haifa)
A. Pnueli (Rehovot)
.G Rozenberg (Leiden)
A. Salomaa (Turku)
C.P. Schnorr (Frankfurt)
* E. Shamir (Jerusalem)
J.E. Vuillemin (Paris)
*( member of the Selection Committee)
Referees for ICALP 81
Albert D. Janko W. Raz Y.
Apt K.R. Jantzen M. Rodeh M.
Jeanrond H.J, Roucairol G.
deBakker J.W. Jerrum M. Rozenberg G.
Bancilhon F. Jones C.
Baudet G.M. Salomaa A.
Becvar J. Kantorowitz E. Salwicki A.
Beeri C. Karhum~ki J. Schnorr C.P.
Ben-Ari M. Kariv O. Schreiber S.
Bergstra J,A. Karp R.M. Schwartz R.L.
Berry G. Katz S. Shamir A.
Beynon W.M. Kleijn H.C.M. Shamir E.
Bird M. Klop J.W. Shields M,W~
Blikle A. Kramosil I. Shiloach Y.
Boehm C. Kreczmar A. Shostak R.
deBruin A. Sippu S.
Bucher W. Lehmann D. Six H.W.
Lempel A. Skyum S.
Cohn A.G. Levy J,J. Soisalon-Soininen E.
Coppo M. Linna M. Steinby M.
Courcelle B. Lipski W. Jr.
Cousineau G. Lozinskii E.L. Thompson C.D.
Cremers A.B. Tiuryn J.
Makowsky J.A. Tucker J.V.
Dembinski P. Manna Z.
Dezani M. Maurer H. Ukkonen E.
Mayoh B.H. Ullman J.D.
Edelsbrunner H. McColl W.F.
Ehrlich G. Meseguer J. Vuillemin J.E.
van Emde Boas P. Meyer J.-J.Ch.
Engelfriet J. Milner R. Wadge W.
Even S. Mirkowska G. Wegner L.
Monien B. Wolper P.
Flajolet P. Monier L.M.
Fraenkel A.S. Muchnick S.S. Yacobi Y.
Francez N. MUller K. Yehudai A.
Yoeli M.
Galil Z. Nivat M.
Gaudep M.C.
Goeman H.J.M. Orlowska E.
Gordon M.J.C. Ottmann Th.
Grabowski M.
deGroote H.F. Park D.
Paterson M.
Harel D. Paz A.
Harrison M.A. Penttonen M.
Havel I.M. Perl Y.
Hennessy M. Perrin D.
Hofri M. Pettorossi A.
Pittl J.
Itai A. Plotkin G.D.
Pnueli A.
Pratt V.
8th International Colloquium on Automata
Languages & Programming
ICALP 81
July 13-17, 1981
Acre (Akko), Israel
TABLE OF CONTENTS
Monday, JulM ,31 Morning
SESSION i: A. Paz, Chairman
C.P. Schnorr
Refined Analysis and inprovements on Some Factoring
Algorit~s ........................................................ I
J. Heintz & M. Sieveking
Absolute Primality of Polynomials i8 Decidable in
Random Polynomial Time in the Number of the Variables ............. 16
F.P. Preparata & J.E. Vuillemin
Area-Time Optimal VLSI Networks for Computing Integer
Multiplication and Discrete Fourier Transform ..................... 29
SESSION :2 F.P. Preparata, Chairman
J.-W. Hong, K. Mehlhorn & A.L. Rosenberg
Cost Tradeoffs in Graph Embedding8, with Applications ........ 41
J.H. Reif
Minimum S-T Cut of a Planar Undirected ~btwork in O(n log2n)
Time .............................................................. 56
E. Welzl
On the Density of Color-Pamilies ............................. 68
Mon~yj July ,31 Afternoon
SESSION :3 R. Sethi, Chairman
C. Beeri & M.Y. Vardi
The Implication Problem for Data Dependencies ................ 73
J.A. Makowsky
Characterizing Data Base Dependencies ........................ 86
M. Sharir
Data Flow Analysis of Applicative Programs ................... 98
SESSION :4 C. Boehm, Chairman
N.D. Jones
Flow Analysis of Lambda Fxpressions ......................... 4 11
J. Loeckx
Algorithmic Specifications of Abstract Data Types ........... 129
P.A. Subrahmanyam
Nondeterminism in Abstract Data Types ........................ 148
IV
~uesday, July ,41 morning_
SESSION 5: E. Shamir, Chairman
J.D. Ullman (Invited Speaker)
A View of Directions in Relational Database Theory ...... 165
C. Reutenauer
i New Characterization of the Regular Languages ......... 177
SESSION 6: H. Maurer, Chairman
J.E. Pin
Langages Reconnaissables et Codage Prefixe Pur .......... 184
J. Engelfriet & G. File
Passes, Sweeps and Visits ............................... 193
Tuesday, July 14_~ Afternoon
SESSION 7: G. Rozenberg, Chairman
S. Sippu & E. Soisalon-Soininen
On LAL~(k) Testing ...................................... 208
E. Ukkonen
On Size Bounds for Deterministic Parse2~s ................ 218
Y. Itzhaik & A. Yehudai
A Decision Procedure for the Equivalence of Two dpdas
One of which is Linear ....................................... 229
SESSION 8: Z. Manna, Chairman
A.R. Meyer, G. Mirkowska & R.S. Streett
The Deducibility Problem in Propositional Dynamic Logic . 238
M. Ben-Ari, J.Y. Halpern & A. Pnueli
Finite Models ~r Deterministic Propositional Dynamic
Logic ........................................................ 249
D. Lehmann, A. Pnueli & J. Stavi
Impartiality, Justice and Fairness: The Ethics of
Concurrent Termination ....................................... 264
Wednesday ~ July 1#, Morning
SESSION 9: K. Mehlhorn, Chairman
A.S. Fraenkel & D. Lichtenstein
Computing a Perfect Strategy for nxn Chess Requires Time
Exponential in n ............................................. 278
O.H. Ibarra, B.S. Leininger & S. Moran
On the Complexity of Simple Arithmetic Expressions ...... 294
M. Snir
Proving Lom~er Bounds for Linear Decision Trees .......... 305
VII
SESSION 10: M. Nivat, Chairman
M. Blattner & M. Latteux
Parikh-Bounded Languages ................................ 316
a. Karhumiki
Generalized Parikh Mappings and Bomomorphisms ........... 324
S. Istrail
Chomsky-Sch~tzenberger Representations for Families of
Languages and Grammatical Types .............................. 333
Thursday, July ~_61 M?rnin~
SESSION ll: J.W. deBakker, Chairman
E. Engeler (Invited Speaker)
Problems and Logics of Programs ................ not included
J.A. Bergstra & J.V. Tucker
Algebraically Specified Progranming Systems and Hoare's
Logic ........................................................ 348
SESSION 12: A.R. Meyer, Chairman
M. Moriconi & R.L. Schwartz
Automatic Construction of Verification Condition
Generators from Hoare Logics ................................. 363
R. Sethi
Circular Expressions: Elimination of Static Envirom~ents 378
Thursdlay, July 16, A~rnoon
SESSION 13: A. Salomaa, Chairman
B. Courcelle
An Axiomatic Approach to the iorenjak-Hopcroft
Algorithms ................................................... 393
E. Ehrenfeucht & G. Rozenberg
On the (Generalized) Post Correspondence Problem with
Lists of Length 2 ............................................ 408
A. Itai, A.G. Konheim & M. Rodeh
A Sparse Table Implementation of Priority Queues ........ 417
SESSION 14: C.P. Schnorr, Chairman
A. Pettorossi
Comparing and Putting Together Secursive Path Ordering,
Simplification Orde~ir{s and Non-Ascending Property for
Termination Proofs of Term Rewriting Systems ................. 432
N. Dershowitz
Termination of Linear Rewriting Systems ................. 448
A. Pnueli & R. Zarhi
Realizing an Equational Specification ............. ...... 459
IIIV
~iday~ July ~71 Mornin~
SESSION 15: A. Pnueli, Chairman
K.R. Apt & G.D. Plotkin
A Cook's Tour of Countable Nondeterminism ................ 479
E.M. Gurari & O.H. Ibarra
The Complexity of Decision Problems for Finite-Turn
MulticounterMachines ......................................... 495
K.N. King
Alternating Multihead Finite Automata .................... 506
SESSION 16: S. Even, Chairman
J. Pearl
The Solution for the Branching Factor of the Alpha-Beta
Pruning Algorithm ............................................. 521
K. Lieberherr
Uniform Complexity and Digital Signatures ................ 530
A. Shamir
On the Generation of CryptoCraphically Strong Pseudo-
Random Sequences .............................................. 544
Errata:
J.A. Makowsky (ICALP 80, pp. 409-421)
Measuring the Expressive Power of Dynamic Logics: An
Application of Abstract Model Theory .......................... 551
Author Index ................................................. 552
REFINED ANALYSIS AND IMPROVEMENTS
ON SOME FACTORING ALGORITHMS
C.P. Schnorr
Fachbereich Mathematik
Univers{tNt Frankfurt
Extended Abstract
Abstract. By combining the principles of known factoring algorithms
we obtain some improved algorithms which by heuristic arguments all
have a time bound O(exp ~c In n in in )~ for various constants c~3.
In particular , Miller's method of solving index equations and Shanks~
method of computing ambiguous quadratic forms with determinant -n can
be modified in this way. We show how to speed up the factorization of
n by using preprocessed lists of those numbers in [-u,~ and
[n-u,n+u],O<<u<<n which only have small prime factors. These lists
can be uniformly used for the factorization of all numbers in [n-u,n+u].
Given these lists, factorization takes O(exp[2(in n)~/3(in in )n 2/3])
steps. We slightly improve Dixon's rigorous analysis of his Monte Carlo
factoring algorithm. We prove that this algorithm with probability I/2
detects a proper factor of every composite n within o(exp ~61n n in in )n
steps.
.I A Refined Analysis of Dixon's Probabilistic Factoring Algorithm.
So far the asymptotically fastest run time of a factoring algorithm
has been proved by Dixon (1978). Given a composite number n, this al-
gorithm finds a proper factor of n with probability I/2 within
O(exp(4~in n in in ~)) steps, in denotes the "logarithmus naturalis"
with the Eulerian number e as base and exp is the inverse function to in.
Dixon mainly applies the method of "combining congruences" to generate
solutions of x2=y2mod n. In Sections 2 and 3 we will see that this
technique can well be combined with factoring algorithms proposed by
J.C.P. Miller (1975) and D. Shanks (1971). We give an outline of Dixon's
algorithm with an improved analysis. We decrease the constant 4 in
This work has been started in Summer 1980 during a stay at the Stan-
ford Computer Science Department. Preparation of this report was
supported in part by National Science Foundation grant MCS-77-23738
and by the Bundesminister fur Forschung und Technologie.
Dixon's bound to~. The improved theoretical time bound results from
a tighter lower bound on the number of quadratic residues mod n which
can be completely factored over small primes (Le~ma )I and a specific
method for detecting small prime factors. Here we do not focus on de-
signing the most practical algorithm but we like to prove a rigorous
asymptotical time bound as small as possible. We do not assume any
distribution on the input data but we assume that some intermediate
data are chosen at random.
Dixon's a!gorithm.
begin input n
stage I v =in I/2r]
comment the optimal choice of r&~ will be made below.
Form the list P of all primes ~v:P={pl,..,p~(v)}.
if ~ pi & P:Piln then print Pi sto~
B:=
stage 2 Choose & z [l,n-l] at random and independently from previous
choices of .z
if gcd(z,n)#1 then print gcd(z,n) stop
w:= z2mod n with O~w<n .a
l
stage 3 Compute a_=(ai6~ Ilgigv(~)) and e w with w=weHiK~(~)pi
and ~p6 P:P does not divide . e w
test I if we#1 then goto stage 2
B:= BU{~},Za:= z
Try to find a nontrivial solution of
= aEBE f~_a _Om°d2; f ~ {0,1}. )I(
test 2 if there is no nontrivial solution then goto stage 2
x:=~fa:iZ ~, y:=~i~(~)pi(Z~ &Bfgai)/2
comment The construction implies x2=y 2 mod n; in case x#±y
mod n, qcd(x±y,n) are proper factors of n.
test 3 f_f_i x#±y mod n then print gcd(x±y,n) stop
Choose the first a~B such that f =I.
-- g
B:=B-{~},goto stage 2
end
Obviously a proper factor of n has been found as soon as test 3 succeeds.
In the following analysis of the algorithm we suppose that n is an odd
number with prime factor decomposition:
