Technical reports on Computer Science

deposit_hagen

Mathematik und

Informatik

Informatik-Berichte 60 – 09/1986

Eberhard Bertsch (Redaktion)

Technical reports on Computer Science

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TECHNICAL REPORTS ON COMPUTER SCIENCE

FERNUNIVERSITÄT HAGEN

The following reports are available free of charge from Prof. Dr. Eberhard Bertsch

Bericht-Versand Informatik Fernuniversität (GH)

D-5800 Hagen

DOBERKAT, ERNST-ERICH

ZUR THEORIE MESSBARER AUTOMATEN UND IHRER TRANSFORMATIONEN, 1980

WEIHRAUCH, KLAUS

EMBEDDING METRIC SPACES INTO CPO-S, 1980

We show that metric spaces with Polish topology (MP) can be represented very well by bounded complete w-algebraic cpo-s with continuous weight and distance

(CWD). An operator r: CWD-MP is defined such that (1) und (2) hold.

(1)

rD

can be embedded topologically into D such that a (partial) function on rö is (metrically) continuous, iff it can be extended to a (total) continuous function on-ir. (2) Every °A"EMP is isometric to some r(O). Therefore the continuous cpo-functions are exactly adequate for describing the continuous functions on the corresponding metric spaces. The approach could be refined in order to study computability on metric spaces with Polish topology. Examples of application are the Euclidean space, the space of total functions (Baire space) and spaces of infinite trees.

NR, 3 DOBERKAT, ERNST-ERICH CONSTRUCTING A HEAP, 1981

Using some ideas from Calculus and Stochastic Processes, the sift-up phase and the selection phase of heapsort are analysed with respect to the average number of comparisons and interchanges. In particular a Conservation of Ignorance Theorem is proved: both phases of heapsort preserve the given distribution of the keys tobe sorted up to a multiplicative constant for scaling.

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NR, 4 DADAM, P,

SYNCHRONISATION IN VERTEILTEN DATENBANKEN, EIN ÜBERBLICK, 1980

First, this paper gives a general introduction to the problems of synchroni- zation in centralized and distributed databases. lt concentrates on the require- ment of ensuring the consistency of the database in the presence of parallel transactions. Subsequently a_ series of different synchronization methods is presented. They differ in the synchronization technique as well as in the pre- conditions. They represent to some extent the state of the art in this area.

From these methods and the applied techniques some basic characteristics are extracted.

NR, 5 DOBERKAT, ERNST-ERICH

INSERTING A NEW ELEMENT INTO A HEAP, 1981

This paper analyzes a well known algorithm which inserts a new element into a heap in such a way that the heap condition is not violated. The analysis is done with respect to the average number of comparisons which are needed to find the correct position for the new element. In contrast to Porter and Simon, who have analyzed this algorithm, too (IEEE Trans. Softw. Eng., vol. SE-1, 1975, 292-298) the present paper gives an explicit formula for the quantities in question (in terms of the binary representation of the number of elements involved). This is done under the assumption that all possible heaps are equally probable and the element tobe inserted is equidistributed, too. Since the com- ponents of the heap are assumed tobe real numbers, the assumption on the distribution must be formulated in terms of Probability Theory, rather than in a combinatorial manner, and consequently methods of Analysis are used rather heavily. Moreover it is shown that the usual finite discrete model for analyzing the average performance of sorting algorithms can be embedded into the model via a functor which preserves probabilities, and expectations.

NR, 6 DOBERKAT, ERNST-ERICH

GOOD STATE TRANSITION POLICIES FOR NONDETERMINISTIC AND STOCHASTIC AUTOMATA, 1980

If the state transitions of a nondeterministic or stochastic automaton are

of interest e.g. if one wants to find an optimal prediction for the next state of a stochastic automaton, or if optimal learning strategies are looked for, when optimality is measured in terms of a given goal of learning. lt is shown in this paper that under some mildly restricted conditions such optimal or nearly optimal state transition policies exist. This is done for stochastic automata. By means of a representation of nondeterministic by stochastic auto- mata - a result which seems tobe of interest by itself - this carries over to

the nondeterministic case. The methods and main auxiliar results come from the theory of set valued maps.

NR, 7 SCHLAGETER, GUNTER

OPTIMISTIC METHODS FOR CONCURRENCY CONTROL IN DISTRIBUTED DATABASE SYSTEMS, 1980

Recently, methods for concurrency control have been proposed which were called

11optimistic^11• These methods do not detect access conflicts when they occur;

instead, a transaction always proceeds, and at its end a check is performed whether a conflict has happened. If so, the transaction is backed up.

This basic approach is investigated in two directions: First, a method is developed which frees read transactions from any consideration of concurrency control; all responsibility for correct synchronization is assigned to the up- date transactions. This method has the great advantage that, in case of con- flicts between read transactions and update transactions, no batkup is performed.

Then, the application of optimistic solutions in distributed database systems is discussed, a solution is presented.

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SCHLAGETER, G,; HAHN, KH1; PRÄDEL, U,;

HÖHE,

J,

EIN FLEXIBLES INFORMATIONSSYSTEM FÜR NICHT-FORMATIERTE UND FORMATIERTE DATEN AUF KLEINRECHNERN,~198O

WEIHRAUCH, KLAUS

REKURSIÖNSTHEORIE UND KOMPLEXITÄTSTHEORIE AUF EFFEKTIVEN CPO-S,

1980

Effective cpo-s are a useful tool for introducing computability on a large class of sets. In this report Blum's theory of computational complexity is generalized to certain effective cpo-s with effective weight. At first, as a generalization

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of Rogers's Isomorphism Theorem for Gödel numberings of the partial recursive functions it is proved that two ¹¹admissible numberings¹¹ of the recursively enumerable elements of an effective cpo are recursively isomorphic. The concept of effective weight on an effective cpo is introduced and recursive cpo-elements are defined. In analogy to Blum's approach two axioms for cpo-complexity are introduced. For cpo-elements with zero weight a hierarchy theorem, the speedup theorem and the gap theorem are proved. Using ¹¹extended¹¹ cpo-s the results can be applied to the recursive elements of a cpo.

NR, 10 DOBERKAT, ERNST-ERICH

DESIGN AND ANALYSIS OF AN OPTIMAL CONTROL ALGORITHM FOR THE OUTPUT OF A STOCHASTIC AUTOMATON, 1980

Given the input-output behavior of a stochastic automaton and a map which

compares output words, optimal controls are introduced, and an explicit formula for such a control is derived by means of linear programming techniques. The second part of this paper deals with the situation that an input and an output word are given and the probability with which the optimal control puts out the word is requested. An algorithm for computing this probability is presented and analysed with respect to its behavior in the worst as well as in the average case.

The latter analysis develops some new techniques, which ar.e necessary since an uncountable variety of possible inputs has tobe considered. These techniques come mainly from real analysis, in particular from measure theory.

NR, 11 BERTSCH, EBERHARD

REGULAR EXPRESSION MATCHING - LANGUAGE CONCEPTS AND EFFICIENT IMPLEMENTATION, 1980

This paper describes a parsing module that is tobe used as rn extension of string processing facilities in progralllTling languages.

The user interface is presented in the well-known framework of regular

expressions. The implementation is sketched in sufficient detail for discussing problems of efficiency. In particular, a linear time bound can be established.

The major novelty lies in the conceptual and implementational structure of parsing results. While preserving a tree-like outside appearance, the key data

NR, 12 SCHNEEWEISS, WINFRID

ALGEBRAISCHE VEREINFACHUNGEN BEI DER GEWINNUNG VON QUASI-MULTILINEARFORMEN BOOLESCHER FUNKTIONEN, 1981

Es wird gezeigt, wie man bei der Berechnung von Multilinearformen oder ver- wandten Formen für boolesche Funktionen bei Zulassung invertierter Variabler zu erheblichen Rechenerleichterungen konvnen kann. Dieses Vorgehen ist besonders deshalb sinnvoll, weil zur Bestinvnung der mittleren Dauer des (logischen)

!-Zustands einer booleschen Funktion ohne weiteres auch gemischte Multilinear- formen aus invertierten und nicht invertierten Variablen benutzt werden dürfen.

Hauptanwendungsgebiete für diese Ergebnisse sind Zuverlässigkeits- und Diagnose- theorie.

Die immer wieder aufgenoltlllene Diskussion eines aus der Literatur bekannten nicht- trivialen Beispiels ergibt erste Eindrücke von der Effizienz verschiedener

Rechenalgorithmen.

NR, 13 DOBERKAT, ERNST-ERICH

NONDETERMINISM OF STOCHASTIC AUTOMATA - AN ETUDE IN MEASURABLE SELECTIONS, 1981

NR, 14 SCHNEEWEISS, WINFRID

KLASSIFIZIERUNG VON ZUFALLSPROZESSEN IM BEREICH DER TECHNISCHEN INFORMATIK, 1981

Es wird ~ezeigt, welche Zufallsprozesse (stochastische Prozesse) an welchen Stellen der Technischen Informatik auftauchen und welche Zusarrmenhänge, ins- besondere Schachtelungen zwischen den verschiedenen Klassen von Zufallsprozes- sen bestehen. Für ein vertieftes Literaturstudium wird auf neuere Lehrbücher verwiesen.

NR, 15 DOBERKAT, ERNST-ERICH

STOCHASTIC AUTOMATA: STABILITY, NONDETERMINISM, AND PREDICTION, 1981

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NR, 16 SCHÄFER, G,,UND WEIHRAUCH, K.

ADMISSIBLE REPRESENTATIONS OF EFFECTIVE CPO-S, 1981

The elements of a cpo (complete partial order) IT are "abstract" objects in general. If we want to compute on a cpo, the elements have tobe represented by "contrete" objects, the machine under consideration can operate with.

In this paper we suggest to choose the set of total functions from IN to IN,IF, as these concrete objects. We define the "admissible representations" 6 :IF-D of an effective cpo by two axioms and discuss this definition. We finally prove that for admissible representations computability on the names coincides with computability on the cpo.

NR, 17 SCHUSTER, HEIDE

DIE HOLLANDER-PUSHDOWN-MASCHINE, 1981

NR, 18 DOBERKAT, ERNST-ERICH

ADDITION VON DUALZAHLEN: BETRACHTUNGEN ZUR MITTLEREN KOMPLEXITÄT EINES EINFACHEN ALGORITHMUS IN DER

SEKUNDARSTUFE II, 1981

Es wird eine einfache Turing-Maschine zur Addition von Dualzahlen definiert, und der maximale wie der mittlere Aufwand für die Arbeit der Maschine wird be- rechnet. Diese Oberlegungen dienen dazu, den Begriff des Algorithmus und seiner Komplexität in mathematisch präziser Weise Schülern im Informatik-Unterricht der Sekundarstufe

II

nahezubringen.

NR, 19 DOBERKAT, ERNST-ERICH

DELETING THE ROOT OF A HEAP, 1981

Using a continuous model, the average behavior of the familiar algorithm for root deletion is considered, when every heap has the same probability to occur.

The analysis centers around the notion of a viable path in the tree represen- tation , i.e. such paths the label which replaces the label of the root may be

allowed to travel when the heap is reconstructed. In case the size of the heap is a power of 2 it is shown that both the expected number of comparisons and of interchanges are asymptotically equal to the respective numbers in the worst case.

NR, 20 DOBERKAT, E,-E,; RATH, P,; RUPIETTA, W,

SIMULATIONSVERFAHREN IM INFORMATIKUNTERRICHT - EIN BEISPIEL-, 1981

Am Beispiel einer Buslinie wird die Entwicklung eines Simulationsprogrammes durchgeführt. Es wird gezeigt, daß vor die Programmentwicklung in der Technik der schrittweisen Verfeinerung eine Phase der scharfen Beschreibung des Problems treten muß. Das Programm wird schrittweise entwickelt, wobei besonderer Wert auf die Interaktion zwischen Algorithmus und Datenstrukturen gelegt wird. Das Pro- gramm wird in der Sprache PASCAL formuliert, die diese Vorgehensweise in beson- derem Maße unterstützt. Abschließend werden Verallgemeinerungsmöglichkeiten diskutiert.

NR, 21 WEIHRAUCH, KLAUS

COMPUTABILITY ON METRIC SPACES, 1981

It is shown that certain effective metric spaces can be reasonably embedded into {weakly) effective algebraic cpo¹s. The construction is similar to that one given by Lacombe, it is, however, more effective. Computability of points and of functions for the metric spaces can be naturally derived from computability for effective cpo¹s, for which a nice theory already exists.

A generalized version of a theorem of Kreisel/Lacombe/Shoenfield can be proved in this framework.

NR, 22 RIESKAMP, M,; SCHLAGETER, G,; PRÄDEL, U,; UNLAND, R, THE NETWORK QUERY LANGUAGE NOAH, 1981

A non-procedural query language for network databases is described. The language is very powerful as compared to other implemented languages. lt allows to formu- late complex queries which, among other things, include conditions for CODASYL- sets and conditions for n:m-relationships. Cyclic databas structures can be

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processed to some extent. This report is not written for the "naive" user of NOAH, and is not meant to replace a NOAH manual. Instead, this report describes the foundations, the underlying concepts, and the structure of the language in more theoretically oriented, technical tenns.

NR, 23 KLINZE, G,

UNTERSUCHUNGEN ZUR IMPLEMENTIERUNG VON VERTEILTEN PROZESSYSTEMEN AUF DER GRUNDLAGE DER DISTRIBUTED PROCESSES, 1982

NR, 24 BRAND, THOMAS; HEIDTMANN, KLAUS D,

THE INVERSION OF SETS BEING DECISIVE OF SYSTEM RELIABILITY

The dependence of system failure on the failures of components can be described by the set of the systems cut sets. Similarly the relationship between the functioning of a system and that of its components is given by the set of its path (tie) sets. If you are for instance interested in the failure mode of a system (perhaps in search of its weak points) and the set of its path is known, you have to derive the set of the systems cut sets from it.

As the structural redundancy of a system is uniquely determined by each of the two sets mentioned above, anyone of them can serve to compute characteristic values of system reliability from corresponding values of its components. The smaller the fundamental sets, the simpler and shorter the computations becomes.

Therefore it is expedient anyway with the exception of trivial cases to derive the set that corresponds to the given or elaborated set and to choose the smaller one. The derivation of one set from the other is called inversion. The method of

inversion described in this paper has been programmed in PASCAL as a systematic and bounded searching algorithm. The presentation of a langer and structured version of this program enables the interested user to understand it and to change it as required, to translate it into another language etc .. The included short form may serve for a quick copy and an easy distribution of the program.

NR, 25 BÄHRING, HELMUT; HEIDTMANN, KLAUS D,

MONOTONE SYSTEME MIT REDUNDANZ-ABHÄNGIGEN KOMPONENTENVERFÜGBARKEITEN

An einfachen und zum Teil aus der Literatur bekannten Beispielen wird gezeigt, wie sich die Verteilungsfunktion der Lebensdauer von Systemen berechnen läßt, bei denen das Ausfallverhalten der Komponenten statistisch voneinander abhängig ist. Zugrundegelegt werden dabei die Verteilungsfunktionen der Komponenten- lebensdauer unter den verschiedenen inneren und äußeren Einflüssen, die auf das System einwirken können. Das Verfahren wird danach allgemein für k-von-n Systeme hergeleitet und an einem Beispiel mit exponentialverteilten Lebensdauern der Komponenten demonstriert. Anschließend wird es auf allgemeine monotone Systeme übertragen.

Die folgende Untersuchung stammt aus dem Bereich der Technischen Infonnatik.

Die gefundenen Ergebnisse sind nicht nur z.B. auf Multiporzessorstrukturen,

sondern allgemein auf technische - ja sogar auf soziologische - Systeme anwendbar.

Deshalb wurde bis auf gelegentliche Randbemerkungen nicht laufend auf die Tech- nische Infonnatik hingewiesen.

NR, 26 PRÄDEL, U,; SCHLAGETER, G,; UNLAND, R, IDEAS ON OPTIMISTIC CONCURRENCY CONTROL I

An inherent weakness of optimistic concurrency control is the fact that the risk of being backed up increases substantially with the length of the transaction.

This paper discusses possible ways of reducing backup risk for long transactions by the use of a timestamping mechanism.

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27

DADAM, P,

SYNCHRONISATION UND RECOVERY IN VERTEILTEN DATENBANKEN:

KONZEPTE UND GRUNDLAGEN,

1982

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NR, 28 KREITZ, CH,; WEIHRAUCH, K,

KOMPLEXITÄTSTHEORIE AUF REELLEN ZAHLEN UND FUNKTIONEN,

1982

Recursive Analysis, the theory of computable real functions and numbers has been studied from various aspects. In this report we investigate computational complexity of real numbers and functions using recursive function theory. We define a constructive representation of real numbers and generalize Blum's theory of computational complexity to computable real numbers. (Partial-) computable real functions are defined using Oracle-Turing-machines and their domains are characterized as the effective G

0-sets. We observe an important relationship between computational complexity of real functions and continuity.

We show that complexity classes of real functions can be defined on effective

K _cr -sets and study conditions which make functions hard to compute.

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29

WEIHRAUCH, KLAUS

ON NATURAL NUMBERINGS AND REPRESENTATIONS,

1982

Basic recursion theory introduces computability on sets like IN,I:* ,2lN, IF :=INN explicitly. Computability on other sets M like finite graphs. rational numbers, segments of ordinals, or real numbers can either be defined explicitly or be reduced to ordi nary recurs i on theory by a numberi ng v : IN --- IM or a represent- a ti on ö: lF --- M.

In the first case a thesis like Church's thesis is needed, in the second case an argument is needed that the numbering (representation) is ¹¹effective¹¹ or

11natural^11• The advantage in the second case is that the theory of computations and computability already exists and that only one function (numbering, repre- sentation) has tobe discussed. Usually concrete numberings are introduced with- out discussion or authors eloquently try to convince·the reader that their number- ings are ¹¹effective¹¹ whatever this means. In this paper a general concept is suggested which explains in which sense many concretely used numberings are effective. By the same idea ¹¹effectiveness¹¹.of representations {e.g. of real

numbers by total functions on IN) can be explained. Examples show the applica- bility of this concept. Finally the connection between certain effective number- ings and representations is discussed. This work extends and generalizes an earlier paper written by the author.

NR, 30 UNLAND, R,; PRÄDEL, U,; SCHLAGETER, G,

IDEAS ON OPTIMISTIC CONCURRENCY CONTROL II: DESIGN ALTER- NATIVES FOR OPTIMISTIC CONCURRENCY CONTROL SCHEMES, 1983

The original approach of optimistic concurrency control has some serious weak- nesses concerning long transactions and starvation. This paper first discusses design alternatives which avoid these disadvantages. Essential improvements can be reached by a new validation scheme which is called snapshot validation. The paper then discusses the use of versions in the optimistic approach in order to free read transactions from concurrency control at all; the proposed concepts does not restrict update transactions.

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NR,31 STETTER, F,

ESTIMATES IN SOFTWARE SCIENCE, 2/1983

A program 1ength estimate which depends on the vocabu1ary size on1y is presented and it is shown that this estimate shou1d substitute the formula based on the count of the operators and operands. Then, the length estimate obtained is used to establish a simple relationship between the vocabulary size. Furthermore, the length estimate obtained can be adjusted such that it is exact at its lower bound, namely for the ease the vocabulary size complies with the potential vocabulary size.

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FOX, D,

EXPERIMENTELLE UND ANALYTISCHE UNTERSUCHUNGEN ZUR EFFIZIENZ VON SPEICHERVERWALTUNGSVERFAHREN BEI TEXT- DATEN, 3/1983

PRÄDEL, U,, SCHLAGETER, G

CONCURRENCY CONTROL IN INTEGRATED INFORMATION SYSTEMS:

A SURVEY OF PROBLEMS, 4/1983

A main stream of research in the area of database systems is the extension of these systems to support non-classical applications like CAD, information systems. The usage of these systems is different in some essential aspects from classical database systems. lt turns out that these different usage patterns have direct consequences for concurrency control. This paper gives a summary of the research problems tobe solved for these integrated informa- tion systems with respect to concurrence control and recovery. lt is not the

intention of the paper to present special solutions, but to characterize the open issues.

NR,34 DETTKI, H,J,, SCHUSTER, H,

REKURSIONSTHEORIE AUF F,

5/1983

In thi s report we deve 1 op a theory for computabil i ty on 1F (where F : = ~"' )

in order to genera 1 i ze the theory of numberi ngs v: ~-M to theory of representations ö : F-M.

We define three fixed representations and show that they are effective in the sence that the utm-theorem and the smn-theorem hold. Reducibility, creative sets, complete sets, and productive sets can be defined. The re- cursion theorem and Rice's theorem can be generalized to precomplete representations.

Furthermore we observe an interesting relationship between the theory of continuity on F with respect to the Baire topology and the theory of computability.

NR,35

DE VRIES, E,

COMPILERBAU MIT ATTRIBUTSGRAMMATIKEN IN LINGUA,

5/1983

Lingua ist ein Compilergenerator auf der Basis attributierter Grallillatiken, der aus der Beschreibung einer Sprachtransfonnation einen Algorithmus kon- struiert, der diese Obersetzung realisiert. Attributierte Gra11111atiken sind dabei sowohl weitgehend als Methode zur Beschreibung der Semantik formali- siert als auch als ein Praxis-und implementierungsnahes Werkzeug im Compiler- bau geeignet. Ein Oberblick über Arbeiten auf dem Gebiet der attributierten Gra11111atiken findet sich in [Raihae 77]. In der vorliegenden Arbeit wird das Konzept der attributierten Gra11111atik beschrieben, seine Realisierung in LINGUA dargestellt und ihr Eingang in den Bereich des Software-Engineering im Compilerbau an Hand einer Demonstrationssprache ausgeführt.

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NR,36 SCHNEEWEISS, W,

TIME REDUNDANCY, 8/1983

In this report some aspects of time redundancy, i.e. the use of extra time to cope with disturbances, are discussed. Specifically, it is supposed that an indivisible task needs t

0 units of time for completion. After a momentary or a finite length disturbance this task has tobe redone from the beginning.

The random variable of primary interest here is the time T

0 needed for the completion of the indivisible task. The probability distribution function and the mean value of T

0 are derived for several models, mostly via two methods to improve the insight into the problems at hand and the trust- worthiness of the derived results.

Another random variable of some interest is the number N of necessary restarts. The probability distribution and the mean value of N are also qerived.

Finally, the case of an interruptable task is investigated. For computa- tional problems, only the pdf of T

0 is given and, in the Poisson case, E(T0) , also E(N) is derived.

NR,37 STETTER, F,

EIN VEREINFACHTES MODELL DER SOFTWAREWISSENSCHAFT,

6/1983

The theory of software science developed by Halstead attempts to analyze the software production process in a unified manner. The theory is based an the assumption that programs are composed of operands and operators.

In this paper we present a simplified view an software science: Weda not distinguish between operands and operators. From there, we obtain simple relationships between programn parameters.

NR,38 RIESKAMP, M, SCHLAGETER, G,

ANFRAGESPRACHEN FÜR NETZWERK-DATENBANKEN:

ÜBERSICHT UND VERGLEICH, 6/1983

Dieser Aufsatz gibt eine Obersicht und einen Vergleich von deskriptiven, nichtprozeduralen Anfragesprachen für Netzwerk-Datenbanken. Die besonderen

Merkmale solcher Anfragesprachen werden beschrieben und in einem Leistungs- vergleich einander gegenübergestellt.

NR,39 BERTSCH, E,

SYNTACTIC OPTIMIZATION OF EXPRESSIONS-AN EXPERIMENTAL APPROACH, 7/1983

Several alternative ways of defining the syntax of expressions in PASCAL are compared.

Based on experimental observations, measures of syntactic efficiency are calculated for each variant of the syntax. An optimal variant is deter- mined for each such measure.

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KREITZ, CH,, WEIHRAUCH, K,

TOWARDS A THEORY OF REPRESENTATIONS, 7/1983

Many mathematicians familiar with the constructivistic objections to classical mathematics concede their validity but remain unconvinced that there is any satisfactory alternative. In this paper we present representa- tions as a foundation for a theory of constructivity in mathematics.

Computability and continuity w.r.t. given representations are defined and studied in connection with reducibility. We investigate topological properties of representations and introduce (continuously-) admissible representations of seperable T

0-spaces.

It is shown that the continuity theory induced by (continuously-)

admissible representations corresponds to the topological continuity theory.

Hence these representations are very appreciate to study constructivity on all kinds of seperable T

0-spaces.

NR,41

STETTER, F,

A MEASURE OF PROGRAM COMPLEXITY,

10/1983

We propose a measure of program complexity which takes into account both the relationship between statements and the relationship between statements and data objects (constants and variables). This measure, called program

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flow complexity, can be calculated from the source text of a program in an easy way.

NR,42

AUGUSTIN, PRÄDEL, SCHOLTEN

MODELLING DATABASE CONCURRENCY CONTROL ALGORITHMS USING A GENERAL PURPOSE PERFORMANCE EVALUATION TOOL,

2/1984

We present a performance evaluation study comparing two often-mentioned concurrency control algorithms, namely (r,x)-locks and OPTIMISTIC con- currency control as proposed by Kung and Robinson. This study was con- ducted by applying a general purpose performance evaluation tool, COPE.

The results show that OPTIMISTIC concurrency control leads to worse database management system performance than LOCKING methods under a wide variety of workload conditions. The application of COPE pointed out how such a study in a very specialized field can be supported by a general tool, and what a general tool is missing for an application to special- ized problems.

NR,43 WEIHRAUCH, K,, KREITZ, CH,

REPRESENTATIONS OF THE REAL NUMBERS AND OF THE OPEN SUBSETS OF THE SET OF REAL NUMBERS,

2/1984

In previous papers we have presented a unified Type 2 theory of computa- bility and continuity and a theory of representations. In this paper the concepts developed so far are used for the foundation of a new kind of constructive analysis. Different standard representations of the real numbers are compared. lt turns out that the crucial differences are of topological nature and that most of the representations (e.g. the decimal representation) are not reasonable for topological reasons. In the second part some effective representations of the open subsets of the real

numbers are introduced and compared.

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KREITZ, CH,, WEIHRAUCH, K,

A UNIFIED APPROACH TO CONSTRUCTIVE AND RECURSIVE ANALYSIS,

2/1984

In the past several attempts have been made to formulate and study con- structivity and computability in mathematics but none of these concepts is generally accepted. In this paper a simple and unified approach to constructive and recursive analysis is presented. Its basis is a standard theory of effectivity on F = {f: lN- J'J} which is formally similar to ordinary recursion theory. lt splits in to a purely topological (11 con- structive11) version and a more special theory of computability.

Effectivity an other sets M is derived by means of representations, i.e.

surjective mappings c5: F--- M, where topological properties of representa- tions play a fundamental role.

As an example representations of the real numbers are studied and it is shown that the significant differences between <previously defined>

representations are topological ones. Finally compactness on the real numbers is studied as a further application of this theory of representa- tions.

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NR,46

STETTER, F,

DOKUMENTE ZUR GESCHICHTE DER INFORMATIK AN DER FERN- UNIVERSITÄT, 3/1984

BERTSCH, E,

LANGUAGE DESCRIPTION AND IMPLEMENTATION CONCEPTS OF LITFAS (LANGUAGE FOR IMPLICATIONS FROM TEXTUAL FILES AND ATOMIC SENTENCES, 4/1984

We define a simple, high-level language that combines essential features of logic prograrrming with a natural file query formalism. The internal sequence of deduction steps is entirely hidden from the user.

A rough outline of the implementation is also presented. lt turns out that the file access mechanism demands a separate kind of backtracking.

Numerous examples are given to demonstrate the expressive power of the language.

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NR,47 BERTSCH, E,, LÄMMERZAHL,J,

EXPERIMENTELLE ERGEBNISSE ZUR EFFIZIENZ DER SUCHE NACH TEILZEICHENKETTEN IN DEUTSCHEN TEXTEN,

7/1984

In diesem Arbeitsbericht wird der Einfluß unterschiedlicher Zeichen- häufigkeiten auf die erreichb~re Geschwindigkeit der Suche nach Zeichen- ketten in größeren Texten untersucht. Obwohl ausschließlich deutsche Texte verwendet werden, sind die eingesetzten Methoden in keinem Punkt von Besonderheiten der deutschen Sprache abhängig.

Die Grundidee besteht darin, statistisch seltene Buchstaben bevorzugt zu suchen. Es zeigt sich, daß eine solche Ausnutzung von bekannten Häufig- keiten zu erheblichen Zeitgewinnen führt. Weiterhin werden die Ge- schwindigkeitssteigerungen untersucht, die durch Vorverarbeitung des- jen1gen Textes, in dem gesucht werden soll, gewonnen werden können.

Hierfür werden mehrere unterschiedliche Ansätze verwendet.

NR,48 KLAHOLD, P,, SCHLAGETER, G,, UNLAND, R,, WILKES, W,, EIN TRANSAKTIONSKONZEPT ZUR UNTERSTÜTZUNG KOMPLEXER ANWENDUNGEN IN INTEGRIERTEN SYSTEMEN,

7/1984

Beim Einsatz von Datenbanksystemen in Anwendungen wie Computer Aided Design, Software Enginieering, etc. stellen die Benutzer wesentlich andere An-

forderungen an die Transaktionskomponente als in korrvnerziellen Umgebungen.

Wichtige Merkmale solcher Umgebungen sind lange Transaktionszeiten und Gruppenarbeit.

In diesem Papier wird ein Konzept für lange Transaktionen vorgestellt, das insbesondere kooperatives Arbeiten von Benutzergruppen auf einer ge- meinsamen Menge von Daten unterstützt. Das Transaktionsmodell ist zwei- schichtig: zum einen muß die Benutzergruppe nach außen hin abgeschirmt werden, zum anderen müssen Mechanismen zur Verfügung gestellt werden, die innerhalb der Gruppe ein kontrolliertes Zusa11111enarbeiten auf ge- meinsamen Objekten erlauben. Im letzteren Falle sind rigide Synchroni- sationsmaßnahmen, wie sie beim Transaktionsmanagment in Datenbanksystemen angewandt werden, nicht brauchbar.

Ein wichtiges Kapitel sowohl zur Unterstützung der Gruppenarbeit als auch allgemein für Datenbanken in Designumgebungen ist ein benutzerorientierter Versionsmechanismus; ein solcher Mechanismus wird vorgestellt und in das Transaktionsmodell integriert.

NR,49 KREITZ, CH,, WEIHRAUCH, K,

COMPACTNESS IN CONSTRUCTIYE ANALYSIS

REYISITED

9/1984

In [5),[3) we have developed a unified Type-2 theory of computability and continuity and a theory of representations. In the paper [6] representa- tions useful for a new kind of constructive analysis were presented. As an application of these concepts we shall now consider constructive compact- ness. We introduce ¹¹reasonable¹¹ representations of closed and compact sets and prove two different versions of the Heine-Borel theorem. Theorems

concerning functions continous on compact sets are investigated relative to constructivity properties and it is shown that usually topological properties (i.e. discontinuity) are the true reasons for nonconstructivity.

NR,50

KREITZ, CH,

THEORIE DER DARSTELLUNG UND IHRE ANWENDUNGEN IN DER KONSTRUKTIVEN

ANALYS

11/1984

Zur Untersuchung von Berechenbarkeit auf überabzählbaren Mengen gibt es bisher eine Reihe unterschiedlicher Modelle aber noch kein allgemeines Kon- zept. Mit der Theorie der Darstellungen wird in dieser Arbeit eine formale Grundlage für eine allgemeine, einheitliche und zugleich einfache Theorie der Berechenbarkeit und Konstruktivität vorgestellt. Ausgangspunkt ist eine

explizite Definition von Effektivität auf der Menge F= {p: ~-:N}. Die so entstandenen Begriffe werden dann auf eine andere Menge M übertragen mit Hilfe von Darstellungen, d.h. surjektiven Abbildungen von 1F auf M. Die so entstehende Theorie ist formal der gewöhnlichen Rekursionstheorie '.echt ähn- lich. Auch topologische Aspekte stellen sich als bedeutend heraus.

Es werden topologische und rekursionstheoretische Eigenschaften von Dar- stellungen untersucht und für einige wichtige Räume gute Darstellungen an-

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gegeben. Am Beispiel konstruktiver Kompaktheit wird die Anwendbarkeit der Theorie für die konstruktive Mathematik demonstriert.

Einzelne Teilaspekte der Theorie wurden bereits in verschiedenen Berichten veröffentlicht [8, 23, 24, 25, 38, 40]. Diese Arbeit faßt die dort ge- wonnenen Erkenntnisse zusalllTien und vervollständigt sie zu einer umfassenden

und geschlossenen Darstellung.

NR,51

NR,52

DEIL, TH,

DARSTELLUNGEN UND BERECHENBARKEIT REELLER ZAHLEN,

12/1984

SCHNEEWEISS, W,

TUTORIAL ON ADVANCED CONCEPTS IN FAULT TREE ANALYSIS,

12/1984

In this report the theory of Boolean functions (of indicator variables) is developed in an extremely economical way to give sufficient insight into consisting of pairwise disjoint tenns (DDNF's).

After that it is shown how easily DDNF's lend to stochastic analysis especially to the determination of the probability of a Boolean function being 1 (which corresponds to system unavilability in fault tree analysis) and of the mean time a Boolean function is O viz. 1 (which corresponds to MTBF viz. MTTR in fault tree analysis.

NR,53

SCHNEEWIESS, W,

THE

TIME-SPECIFIC FAILURE FREQUENCY

OF REPAIRABLE

SYSTEMS WITH STOCHASTICALLY INDEPENDENT COMPONENTS,

2/1985

lt is shown how the time-specific failure frequency of a repairable system can be calculated from the reliability structure function (or fault tree) of the system and the renewal densities of the alternating renewal processes of the components. (lt is discussed why results are restriced to the case of stochastically independent components.)

NR,54 KLAHOLD, P,, SCHLAGETER, G,, STRIEWE, H,-J,

STRING SEARCHING ALGORITHMS: IMPROVEMENTS AND EXPER- IMENTAL RESULTS, 5/1985

Fast string searching algorithms play an important role in many application areas. In this paper the published algorithms are surveyed, considerable im- provements are developed, and a detailed experimental comparison of the algo- rithms is presented. Some of the improvements as well as same of the results of the measurements are quite surprising, among these that algorithms for multiple-words at-a-time seach cannot compete with repeatedly applied one- word at-a-time algorithms in practical situations. As a conclusion we present

concise criteria for the selection of the approriate algorithm for a given application.

NR,55 SCHNEEWEISS,W,

BASIC ASPECTS OF AN EXTENDED RELIABILITY ANALYSIS OF A HAFTLAN (HOMOGENEOUS AUXILIARY FAULT TOLERANT LOCAL AREA NETWORK), 6/1985

This is the basic report of an investigation of the fundamental reliability characteristics of HAFTLANs for single fault tolerance in connection with 1-diagnosability. lt is shown how fault trees or equivalent graphs can be found for such system and how reliability characteristics such as avail- ability and failure frequency can be deduced. Furthermore, some thoughts on system self-diagnosis and on well organized routing even in cases of certain component failures are co111J1unicated.

NR,56 SCHLAGETER, G,,STERN, W,

DIE GROSSE CHANCE FÜR DEZENTRALE AUSBILDUNG: BILD-

SCHIRMTEXT, ÜBERLEGUNGEN AM BEISPIEL DER FERNUNIVERSITÄT,

11/1985

Für dezentrale Formen der Aus-und Weiterbildung spielen elektronische Medien in schnell zunehmenden Maße eine wichtige Rolle. In dieser Arbeit werden Ein- satzmöglichkeiten des Mediums Bildschirmtext (BIX) skizziert, mit welchem sich - insbesondere im Bereich der Weiterbildung -wesentliche Verbesserungen gegen -

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über herkömmlichen Systemen erreichen lassen. Von besonderer Bedeutung ist dabei das "intelligente" BTX-Endgerät oder der BTX-fähige Personal- computer, mit dessen Hilfe Konzepte des computer-unterstützten Unterrichts

(CUU) erstmalig in dezentralen Ausbildungsformen realisiert werden können.

NR,57

WEIHRAUCH, K,

A SIMPLE FORMALISM FOR SOLVING DOMAIN EQUATIONS,

11/1985

The purpose of the theory of domains is to give models for spaces which are used for denotational semantics of programming languages (Scott and Strachey [1], Stoy [2], Gordon [3], Tennent [4]). The kinds of spaces which are needed involve spaces of higher functiona1 types and spaces defined recursively.

Several strategies have been proposed for finding suitable spaces which satisfy the desired recursion equations (Scott [5], [6], [7], Sanderson [8]). It has been suspected already for a long time that the theory of domains itself can be applied for solving recursive domain equations. Scott [7] remarks that

domains can be made into a domain and outlines roughly his ideas. In this paper a computable "super-cpo" "Us is defined which essentially consists of all

"constructive domains". Domain equations and domain ¹¹isomorphisms¹¹ correspond to fixed point equations on "Us which can be solved effectively by methods well know from cpo theory. The formalism is very simple and describes adequately naive constructions for solving domain equations.

NR,58

KLAHOLD, P,,SCHLAGETER, G,, WIKES, W,:

A GENERAL MODEL FOR VERSION MANAGEMENT IN DATABASES,

3/1986

In this paper we introduce a general model for version management expressed by the concept of version environments. Aversion environment offers two

mechanisms for structuring the version sets of objects: graphs and partitions.

By the use of views, constraints and transactions the version environment may be tailored to specific user requirements. The embedding of applicatio~ tools into the version environment provides the user with their specific application environment which consists of the objects, their version structures and the

tools operating on them. The proposed concept is more general and more power-

ful than the concepts published so far; it is shown, how well known version concepts can be implemented by means of version environments.

NR,59 MÜLLER, N,TH,

COMPUTATIONAL COMPLEXITY OF REAL FUNCTIONS AND REAL NUMBERS, 6/1986

Computability and complexity of real functions and real numbers are studied in a model where methods of recursive function theory as well as methods of numerical analysis can be used at a very low level of complexity. Topological properties turn out tobe important for computational questions as well as for questions of existence of complexity bounds. As an example of application the computational complexity of the roots of real functions is studied with respect to the analytic properties of the functions.

NR,60 ABSTRACTS DER INFORMATIK-BERICHTE

1-59

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