Development of Rigorous Adaptive Information Systems

Rigoros and Adaptive ... Information Systems 1

Development of Rigorous Adaptive Information

Systems

Dr. Nasreddine AoumeurFIN, ITI, DB group

[email protected]

Course Site: wwwiti.cs.uni-magdeburg.de/~aoumeur wwwiti.cs.uni-magdeburg.de/iti_db/lehre/oois/inde


Information Systems: Working Information Systems: Working definitiondefinition

– reactive systems (i.e. in continuous interaction with their environment), with

– large amount of immutable and non-immutable data (i.e. fixed and changing) and, with

– processes and activities for exhibiting behaviors on these (state-less and –full) data.


Different generations of CMs : “Entity first”

State-less and -ful DATA

Processes and Rules

IS Conceptual ModelEntity-Relationship[1973..] - Intuitive / Simple - Revolutionary for IS - UoD : Entities+Relations - Mathematically sound - Rich abstraction mechnanisms - Different variants (NIAM / SADT / MERISE / ..)

Process-centric Formalisms - CCS, CSP, DFD, Petri Nets, .. - Synchronous / asynchronous - Mathematically sound - Executable / operational


Different generations of CMs : “Object first”

State-less and -ful DATA

Processes and Rules

IS Conceptual Model Object Paradigm[1980..] - Really Intuitive / highly accepted - Object (Id, structure / dynamic) - UoD : Interacting objects community - Rich abstraction mechnanisms (e.g. Class, inheritance, role, aggregation, ..)

- Different formal interpretations

Behavior-centric OO Formalisms - OO Petri Nets, Mondel, JSD.. - Mathematically sound - Executable / operational / concurrent - Cope with data and process around objects


Current generation of CMs : “Interaction first”

Aspect-/connector-/meta-level

All What is : - Evolving (business rules, market laws, cross-organizational policies, …) - Cross-Cutting (security, management,..)

- Non-functional (availability, performance,..)

Stable and invariantentities

IS Conceptual ModelAspect/archietctural Paradigm - Explicit separation between Coordination and computation - Separation between what is evolving from what is stable - Dynamic shifting-down / up of changing behavior - Suitable for services and mobility

Entity Interfaces

Dynamically weaving


First generation of CMs : “Entity first”

Processes and Rules

E/R Conceptual Model

Entity Name

Attribute1 : Type1

Attribute2 : Type2....Attributei : Typei

Property1

.....

n-m

i-j AssocPART

IS-A

m Entit(ies)

n Entit(ies)


First generation of CMs : “Entity first”E/R Conceptual Model

Customer

Name : StringBirth-Date : DateAddress : AddressIncome : Money

Open-Date

Bank

1-20-N Own

(Running) Account

Number : NatBalance : MoneyLimit : MoneyHistory : List[Date,Money]

IS-A

Saving Account

Number : NatInterest : PercentBalance

Processes and RulesAccount USE : First open --- then deposit – then (withdraw-deposit)* - then Close-or-be-closed



Customer

Name : StringAmount

Date

1-20-N Withdraw

AutomaticTellerMachine

ATM-Reference : StringCash : HiddenBank : StringTransaction : List[Money]History :List[Card-Nb,Acnt-Nb,Money

Bank-Card

Number : NatAccount-Nb: NatCode : String

Processes and RulesATM-use : First enter-card – then enter-code – then enter-transaction—get money



Student

Name : StringSubscription-NbSemester

Date-Out

Date-Back

0-N0-3 Borrow

Book

Reference : StringName : StringAuthor : StringPublisher : String

Processes and RulesFirst subscribe-- Get library-card – (Borrow – Return –or– Penality)*--(be)Unsubscribe(d)


First CM generation : Process With Petri NetsWhat is a behavioral process in IS---at the

highest-abstract-level?

• States (instances) : In terms of (un-)availability. That a state instance is regarded as a resource

- Example : An account (instance) is a resource, a book (instance) is a resource.

• (State-based) Actions: The allowed ordering causality between states (instances) via actions (i.e. operations, methods).

- Example : First open-account, then deposit then looping withdraw-depsit-then close


• Author : Carl-Adam Petri Live currently in Hamburg (honorary Professor at the Univ.)

• History: Model introduced by C.A. Petri in 1962– (Physics) Ph.D. Thesis:

“Communication with Automata”• PNs Applications: Distributed computing,

manufacturing, control, information systems, communication networks, transportation…

• Purpose: PNs specify / validate / verify explicitly and graphically:– sequencing/causality actions on states– conflict/non-deterministic choice actions– True concurrency actions on states

First CM generation : Process With Petri Nets


(Introductory) Reference:• Tadao Murata. “Petri nets: Properties, Analysis

and Applications.” Proc. of the IEEE, 77(4), 1989.• Wolfgang Reisig, “Petri Nets”, Springer, EATCS

Monographs on Theoretical Computer Science, 1985 (Also in German).

First CM generation : Process With Petri Nets


First CM generation : Process With Petri NetsConceptual philosophy under Petri nets:

1. In any system, we have resources- Artifact-based resources : data, objects,

events, - Real resources : printers, buffers, CPUs

2. There is generally, a number of available instances for each kind of resource in the system.

3. Actions (behavior, dynamics) in the system allows: - consuming (using) some resources and- producing new ones or updating existing

ones (under some conditions).


• With each kind of ressource is described by:– a PLACE graphically as circle is associated

• Ressource instances are included as:– BLACK DOTS (called TOKENS) within the corresponding

ressource kind place.

• Actions called TRANSITIONS are:– graphically represented as a BOX or RECTANGLE.

• Ressources consumption are captured by:– INPUT ARCS---valuted or inscribed by the numbers of

required ressouces--- From the corresponding ressource place to the associated action box.

• Ressources production or changes are captured by:– OUTPUT ARCS---valuted or inscribed by the numbers of produced

ressouces--- From the associated action box to the corresponding target resource place

PETRI NETS ARE BIPARTITE GRAPHS

First CM generation : Petri Nets Concepts


First CM generation : Petri Nets Concepts

2

4

30

P1

P2

T1

INPUT place withfive (5) tokens as MarkingINPUT place withfive (5) tokens as Marking

INPUT arc withtwo (2) (required tokens) as arc-inscription

INPUT arc withtwo (2) (required tokens) as arc-inscription

Transition named T1Transition named T1

OUTPUT arc withFour (4) (produced tokens) as arc-inscription

OUTPUT arc withFour (4) (produced tokens) as arc-inscription

OUTPUT place withthirty (30) tokens as markingOUTPUT place withthirty (30) tokens as marking


First CM generation : Petri Nets Illustrations

BankOKToOpen

OpenAcnt

DepositOpened

AcntState

Withdraw DepositTransfert

Closed


First CM generation : Petri Nets Illustrations

1

1

30

Books@LibraryToBorrow

Borow

1B

orro

wed

-Boo

ks

ToReturn

Return Return&Penalty

Penality2Pay

6

Card


First CM generation : Petri Nets Strenghts

t1

t1 t2 t3

(b) Conflict t1 t2 t3

t2

© Concurrency

(a) Sequencetial execution

and choice


First CM generation : Petri Nets Strenghts

t1 t2 t3

t1

t4

(d) Synchronation (e) Merging


First CM generation : Petri Nets Typical Use

ToSend

Send msg

Receive Ack Send Ack

Receive msg

ToReceive

CommunicationProtocols


First CM generation : Petri Nets Typical UseOperating Systems

Produce

Consume

Buffer


First CM generation : Petri Nets Typical UseEmbedded Systems

Coins

Change

GetCigarett

e

GetCaffe

Machine-Items

GetWater

2$4$3$

75P

25P

Water Cigarette

Caffe


First CM generation: Petri Nets FormalismsA Petri nets in a five tuples PN = (P, T, W, M0)

– P = {p1,p2, ....,pn} is a finite sets of places (circles)– T = {t1, t2, ...,tq} is a finite set of transitions

(boxes)– F (P x T) (T X P) is a finite set of arcs. An input

(resp. output) ) arc joins a place to transition (resp. transition to place). NEVER PLACE TO PLACE or TRANSITION TO TRANSITION.

– W : F {1,2,...} is a weight function attached to the arcs. If the weight in missing it is implicitly one.

– M0 : P {0,1,2,....} is the intial marking. M0(p), p P is the marking (i.e. numbers of tokens) of the place p.


First CM generation: Petri Nets FormalismsNotations :

t : the set of input places of transition t. that is the set of places p such that (p,t) F.

– t : the set of output places of transition t. That is, p such that (t,p) F.

p : the set of input transitions of place p. that is the set of transitions such that (t,p) F.

– p : the set of output places of transition t. That is, t such that (p,t) F.


Dynamics of Petri nets :– A transtion t is said to be enabled if, whatever

p t , p contains a number of tokens greater of equal than W(p,t) (i.e. M(p) W(p,t))

– Firing an enabled transition t, consists in :»Removing W(p,t) tokens from each p t »Adding W(t, p) tokens from each p t »That is, M‘(p) = M(p) – W(p,t) + W(t,p)

– A sequence of transitions firing is generally represented by = <ti1, ti2 , ....., tik>, and

– We say that the corresponding resulting marking is: M0 -- --Mk

First CM generation: Petri Nets Dyanmisms


First CM generation : Petri Nets DynamismsOperating Systems Animated

Produce

Consume

Buffer


First CM generation : Petri Nets DynamismsEmbedded Systems Animated

Coins

Change

GetCigarett

e

GetCaffe

Machine-Items

GetWater

5$4$3$

75P

25P

Water

Cigarette Caffe

1810 67

111

100

2

2

175


H2

O2

H2O

t

2

2

First CM generation : Petri Nets Dynamisms

Chimical Reactions : 2H2 + O2 2H2O


Incidence matrix : A = [aij]

– is an n m matrix of integers – its typical entry is given by

aij = aij+ - aij

-

– Where aij+ = w(T,P) is the weight of the

arc from transition T to its output place P

– and aij- =w(P.T) is the weight of the arc

from the input place P to the transition T.

First CM generation : Petri Nets Internals


• Given an initial marking M0, let be a firiable sequence of transitions which applies to M0.

• The counting vector V of is the vector V = [v1,v2,..,vj,...vq] is the numbers of times tj is included in .

• If M is the marking obtained by firing , then: » Mt = M0

t + AVt .

With t denotes the transpose.



Illustration:

2t1 p1 t2 p2 t4

t3 p3

p4

4

2

2



t1 t2 t3 t4 p1 1 -2 -1 0 • A = p2 0 4 0 -1 p3 0 0 1 -1 p4 0 0 -2 2

Let M0 = [3,0,0,2] and = <t2,t3,t4>,

that is V = [0,1,1,1] .

Then M = [0, 3, 0, 2] using the formulas.


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Development of Rigorous Adaptive Information Systems

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