international workshop on software design and architecture...

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INTERACTIVE SYSTEMS: PRINCIPLES AND ARCHITECTURES

Tutorial

International Workshop on Software Design andArchitecture (SoDA 04)

Srinath SrinivasaIndian Institute of Information Technology, Bangalore

India 560100

[email protected]

http://http://www.iiitb.ac.in/mailto:[email protected]

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OUTLINE

• Interactive dynamics, informally...• Conceptual differences between interactive and algorithmic

dynamics

• Interactive dynamics in practice: closed systems vs open sys-tems

• Principles of Open Systems• A meta-model for open systems design

http://http://www.iiitb.ac.in/

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COMPUTATION

A mechanical procedure for mapping between a given “prob-lem” statement and its “answer.” Usually represented in theform of functionsf : I → O, whereI is the input “problem”domain andO is the output “solution” domain..

Different connotations of computation:

1. Decision

2. Classification

3. Calculation

4. Search

5. ...


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EXPRESSIVENESS OF A COMPUTATIONAL MODEL

The expressivenessof a computational model is defined as the “class” ofdecision problems that they can solve.

An expressiveness hierarchy of computational problems:

Regular ← Context Free← Recursively enumerable← Recursive

DFA,Regular expressions ← context free grammar, PDA ←Turing recognisers← Turing enumerators


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THE TURING MACHINE

The mathematical model of computation is the Turing Machine which is of theform: TM = (S, T, s0, δ,H) where:

S is a set of TM statesT is a set of tape symbolss0 ∈ S is the start stateδ : S × T → S × T × {L,R} is the transition functionH is a set of halting states.

A TM uses an infinite tape on which the input is provided as afinite sequenceof symbols. The TM always begins computation ats0 and the TM finishescomputation when it reaches any stateh ∈ H.

Important: A TM hasto necessarily halt for the computational problem to be

termed “decidable.” If the TM cannot halt then the problem instance is said

to be “undecidable.” (This is the basis for the difference between sets that are

recursively enumerable and sets which are recursive).


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VARIANTS OF TURING MACHINES

• Turing recognizers (decides for all inputs)

• Turing enumerators (recognizes all valid members)

• Universal Turing Machine (loads the specification of another Turing Ma-chine and executes it)

Computers today is termed to be no more powerful than theUniversal Turing

Machine


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EQUIVALENT MODELS OFCOMPUTATION

• λ-calculus• First order logic, algebras and induction• Conventional (well-founded) set theory• Functional and imperative programming (Pascal, C, Lisp,

etc.)


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EXAMPLES OF COMPUTATION

square(int x) returns the square of an integerx. Hencesquare(9)→ 81

gcd(int x, int y) computes the gcd of two integers. Hencegcd(10, 25)→ 5

shortestpath(graph G, node x, node y) computes theshortest path between nodesx andy in a given graphG.

Do all computers only compute?


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EXAMPLES OF COMPUTATION

Consider the following problem:

Design an function for a robot to navigate from a givensource to a given destination in a dynamic environmenthaving moving objects.

Inputs: source, destination, map of the environment, dynamic objects in en-vironment, formula about dynamics of objects in environment, formula aboutinterference between dynamics of objects, ...

What is the complexity of designing such a function?

(Yet, software for robotic navigation is quite common – because they useinter-

activemodels of robot dynamics.)


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PROPERTIES OFCOMPUTATION

Mathematically, computation is defined by several models andset-theoretic notations. These models have the following proper-ties:

1. The specification of the problem is of finite length (although the workspaceneeded for computation may itself be infinite)

2. All data relevant to the problem is available at the beginning of computation(Closed-world assumption)

3. No exchanges of intermediate results take place with external environmentsuntil computation finishes

4. All valid computations terminate

5. The computation is stateless – multiple invocations of the same problemwith the same input parameters produce the same results.


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DOMAIN -THEORETIC NOTION OF COMPUTATION

s0 : start state

h0 h1 h2

Each point in the domain represents data exchange with the ex-ternal world. Computing domains are always “pointed” domains.


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THE STRUCTURE OF A COMPUTATIONAL SYSTEM

s0 : start state

h0 h1 h2

s0 : start state

h0 h1 h2

s0 : start state

h0 h1 h2

s0 : start state

h0 h1 h2

s0 : start state

h0 h1 h2

s0 : start state

h0 h1 h2

Pure computational systems form perfect hierarchies with severallevels of pointed domains. The relationship between two compu-tational process is in the form of subroutine calls.


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INDUCTIVE CHARACTERIZATION OF COMPUTATION

Computation can be represented as a set comprising of(problem, solution) pairswhich can be defined inductively. Induction has the following steps (Considerthe definition of the computationSQ defined asy = x2):

1. Initial condition. ((0, 0) ∈ SQ)

2. Iteration condition. (if(x, y) ∈ SQ then so does(x+ 1, y + 2x+ 1))

3. Iteration condition. (if(x, y) ∈ SQ then so does(−x, y))

4. Minimality condition. (The only elements ofSQ are those which are de-fined by the above two steps)

Minimality is a characteristic of computation. A computational system forbids

any element that it has not explicitly permitted as part of its computational rules.


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INTERACTION

Almost all real-world processes areinteractivein nature.

Interaction involves at least two actors, neither of whom have absolute controlover the interactive process.

For any actor, interaction requires exchange of intermediate results with one ormore external environments.

Intermediate inputs from the environment(s) may be related to the intermediateresults. (Hence they cannot be bundled into one input packet at the beginning).

The system has no control over the behaviour of its environment(s).


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CONSIDER THE FOLLOWING SCENARIOS...

Bob: What is your name?

Alice: Usually the train arrives on time.

Bob: Where did you study?

Alice: It never rains in November.

Bob: How do you like it here?

Alice: Canberra is the capital of Australia.


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Alice: Alice

Bob: What is the capital of Australia?

Alice: Canberra.


Alice: Alice

Bob: What is the boiling temperature of water?

Alice: 100 degrees


Alice: Alice


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Alice: Alice


Alice: IITM

Bob: Where is it?

Alice: In Chennai, India.


Alice: 100 degrees

Bob: What is it in Farenheit?

Alice: 212 degrees

In which of the above three scenarios, do you think Bob and Alicewereinteracting?


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INTERACTION

Interaction involves a persistent state that is shared across all in-teracting actors.


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COMPUTATION + PERSISTENT STATE

What can a persistent state do?

• A persistent state captures the (gist of) history of all previouscomputations.

• The behaviour of an interactive system is not only dependenton the input problem, but also on the contents of the persistentstate. (Remember the ATM telling you, “Sorry, you are notallowed to withdraw more than Rs. 10,000/- in a week”?).

• In effect, a persistent state results in a different start state foreach computation.


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DOMAIN CHARACTERISATION OF COMPUTATION+PERSISTENT STATE

s0

s67

s82

s43s112

s18s5

Interaction

Interaction

Interaction

InteractionInteraction

InteractionInteraction

With a persistent state, there is no single start state for computation. The domainmay be arbitrary in shape. In fact, it could also benon-wellfounded.In domain theoretic terms,x ⊂ y means thaty is higher in the domain (containsmore information, etc.) thanx. And,x ⊂ y, y ⊂ z ⇒ x ⊂ z.In a well-foundeddomain, for anyx, x 6⊂ x. But in the above domain, it is wellpossible thatx ⊂ x. (In the example,s0 ⊂ s0).


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CHARACTERISTICS OF COMPUTATION+ PERSISTENT STATE

1. No single start state (in fact, there could be an infinite numberof start states!)

2. Computation has to terminate, but the interaction itself neednot terminate. It could go on forever!

3. No nice hierarchical structures. Processes have acoroutinerelationship with one another (with the subroutine relation-ship being a special case).

How do we deal with infinite states?In many cases, an infinite state space can be partitioned into a finite numberof state classes. (Ex:income ≤ 1, 50, 000, 1, 50, 000 < income ≤ 5, 00, 000,5, 00, 000 < income)

But such partitioning is not possible always.


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INDUCTIVE CHARACTERISATION

Consider the way computationSQ is characterised:

s0 (0,0)

Rule 1

s1 (1,1)

Rule 2

Rule 3 s2 (−1,1)

Rule 2

Rule 3

Rule 2

(2,4) Rule 3

Rule 3

s4 (−2,4)

Rule 2

s3


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INDUCTIVE CHARACTERISATION

A member of an inductive domain is characterised by the pathsleading to it from the initial elements.

s3 = s0 + Rule 2 + Rule 2s4 = s0 + Rule 2 + Rule 2 + Rule 3 = s3 + Rule 3

(s3, Rule 3)→ s4


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COINDUCTIVE CHARACTERISATION

United States of Utopia

u0 u1 u2 u3

p0

p1

p2

Rule 1

Rule 2 Rule 1

Rule 3

Rule 1 Rule 3

p3


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COINDUCTIVE CHARACTERISATION

1. Set of final elements (u0, u1, u2, u3) and rules of the negative

2. Set of elements and rules for “unfolding”[p0, (Rule 1→ u0)][p3, (Rule 1 +Rule 1→ u0), (Rule 3→ p2)]

3. Maximality condition

Coinductive domains have amaximality conditionthat permits any element (andits corresponding unfolding) unless it is explicitly forbidden by the model.

State s in an inductive description:s is that state which results after applyingthe following rules from the initial state.

State s in a coinductive description:s is that state from which, the followingbehaviours can take me to utopia..


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COINDUCTIVE CHARACTERISATION: EXAMPLE

• Final conditions:Grade = {A,B,C,D}

• Once a grade is decided, it cannot be upgraded (i.e. B cannot be upgradedto A)

1. Element A: If student does not have 85% attendance s/he gets grade B.

2. Element B: If student does not have 85% attendance s/he gets grade C.

3. Element C: If student does not have 85% attendance s/he gets grade D.

4. Element “Local student”: If student has consistently scored above 90% inall tests s/he gets an A.

5. Element “Local student”: If student has consistently scored below 40% inall tests s/he gets a D.

6. Element “Local student”: If student’s average score occurs in the first quar-tile of class scores s/he gets an A.

7. ...


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A B C D

Local Student

1 2 3

4, 6 5


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A B C D

Local Student

1 2 3

4, 6 5

Unregistered Student

Foreign Student

Research Student

There is no single starting point for computation. Computation may start from

different places depending on whether the student is a local registered student, a

local research student, an unregistered student or a foreign student.


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INDUCTION VS COINDUCTION

Induction: Construction metaphor. (The “unfolded behaviour” of an inductivesystem is defined by the base conditions and construction rules)

Coinduction: Observation metaphor (The rules of the system are designed such

that they produce the speficied “unfolded behaviour.”)


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COINDUCTIVE CLASS SPECIFICATION LANGUAGE

The observable behaviour of a method is defined as the unfolding behaviour ofthe object from the point where it was called.

Consider a vending machine object having methods:insertcoin(), choose(),option(), commit().

The object is considered as a set of all possible valid streams of be-

haviour. A call to insertcoin() for example returns a stream of the form:

(insertcoin(), choose(), option(), commit())


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EXAMPLES OF COMPUTATION+ PERSISTENT STATE

1. C function with static variables

2. A read-write database engine

3. Objects...

Open Systems:A system whose behaviour is best specified coinductively is

also termed an “open” system. The system is by definition open to addition of

behavioural “starting points” (and possibly removal of old “starting points” that

are no longer relevant)


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WHY IS THERE NO SILVER BULLET FOR SOFTWARESYSTEMS?

Fred Brooks’ contention of “no silver bullet” for building software systems stillseems to hold

Consider how objects are designed:

1. The behaviour of an object is considered to be abstracted by its interface

2. Object interface contains only method signatures. Method calls can manip-ulate the object’s state; however the state itself ishiddenfrom the externalworld

3. Specifically,there is no provision to specify different “starting points” ofcomputation

There is no silver bullet because we try to model open systems using closed

models. (Note that using an open model does not automatically bring a silver

bullet – there may be an infinite number of starting points..)


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SERVICEOBJECT: A NEW MODEL FOR OBJECTS

ServiceObject = set of “starting points” orstates

State =(Condition, {(methodsig, endstate)}) whereCondition is the enabling condition for the state (condition that needs to

uniquely hold for the object to start from this state)

methodsig is the signature of a method that the state supports andendstate is a

state of the object that can be reached on calling this method. Obviouslyendstate

should be already defined in the object.


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Object Interface:

Object id

...

...

...

State id

Condition

method()method()

...

State id

Condition

method()method()

...

method()

method()...

Methods that arenot dependent on starting points


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Qualifiers for states:A state (“starting point”) can be qualified as..

• Private: This state is not “visible” to the outside. The service objectcannot be instantiated to start from this state. This state can be reached byother states. They cannot be inherited by derived classes.

• Public: This state is visible to the outside. Objects can be instantiatedto start from this state. They can be inherited by derived classes.

• Protected: This state is not visible to the outside; but they are inherita-ble by derived classes.

Inheritance:If B is a derived class ofA then..

• B inherits all public and protected states ofA. It can override the startcondition and method definitions if they are also either public or protected.

• B can add more states (more starting points) and methods to the class.

• Wherever an object ofA is required in the system, an object ofB can besubstituted without loss of semantics.


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ADDITION OF STATES

As in Java, each service class should be derived from a single top-most superclass ServiceObject.

ServiceObject supports the methodaddState(State s) that adds statesto the object.

Each state is derived from a super class State that supports a methodbooleangetCondition() which returnstrue if the enabling condition holds, orfalse otherwise.

When a service object is initialised, it executes anif ... else laddercalling getCondition() on each of its states to determine which should bethe starting state.

ServiceObject also supports methodsetState(State s) where the state of

the object can be explicitly set to states from the present state (sayt ). setState

succeeds only if the enabling conditions ofs and t are independent of one

another.


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DESIGNING INTERACTIVE PROCESSES: EXAMPLE

Consider the problem of a student joining an institution like IIT. A typical work-flow engine would divide this process into several tasks and order them in someconsistent order. For example:

1. Obtain admission form from admin office

2. Submit filled admission form along with original certificates to Registrar

3. Obtain medical test form and insurance form from admin office

4. Undergo medical test and hospital and get report

5. Submit insurance form with medical report to admin

6. Obtain hostel form from admin office

7. Submit filled hostel form to hostel warden

8. ...

Usually, the admission process never happens in exactly the above sequence.

However, if a workflow engine (built using an inductive model) is used, it would

generate forms strictly in the above order..


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DESIGNING INTERACTIVE PROCESSES: EXAMPLE

1. Identify the end state:all-formalities-over

2. Identify negatives:There should never be a state where hostel and insurance processes havecompleted, but admission has not been completed.

3. Identify states and unfolding behaviours:

• State:insurance-overCondition:{admin− over, insurance− pending}Method:next()→ {all− formalities− over, hostel− pending}• State:insurance-pending

Condition:{admin− over}Method:getInsuranceform()→ medicaltest− pendingMethod:submitInsuranceform()→ {insurance− pending, insurance− over}• State:only-medicaltest-pending

Condition:{admin− over, insurance− pending}Method:getInsuranceform()→ medicaltest− pendingMethod:submitMedicalReport()→ insurance− pending• ...• ...


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CONSIDER THE FOLLOWING SCENARIOS


Alice: Alice


Alice: IITM

Bob: Where is it?

Ashok: In Chennai, India.


Ashok: 100 degrees

Bob: What is it in Farenheit?

Alice: 212 degrees


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CONSIDER THE FOLLOWING SCENARIOS


Alice: Alice

Bob: What isyour name?

Ashok: Ashok


Alice: IITM

Bob: And how about you? Where did you study and what was your branch?

Ashok: IITB, Computer Science and Engineering

Bob: Do you think you can finish this project?

Alice: Yes, I have the confidence..

Ashok: We are IITians; we are trained to sleep only on national holidays... ;)

What is the difference between this and the earlier interaction?


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MULTI -STREAM INTERACTION

When interaction happens among only two actors; or when interaction among

multiple actors is in a broadcast mode, it is calledsingle-streaminteraction. In

multi-streaminteraction, each interacting actor has its own “view” of the global,

shared persistent state


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PROPERTIES OF MULTI-STREAM INTERACTION

1. Multi-stream interaction = computation + persistent state +channel sensi-tivity

2. It is not only important to computewhat the answer is, but alsowho theanswer should go to

3. Response to an input on a channel is dependent on: input parameters, his-tory of previous interactions, interactions taking place on other channels(hidden adversary versus hidden variable)

4. Almost all information systems are multi-stream interaction machines

5. Examples of multi-stream interaction machines:A set of objects belonging to the same class, sharing class (static) variablesMulti-user read-write database systemsUnix and any multi-user operating system


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META-MODELS SUPPORTING INTERACTION CHANNELSEXPLICITLY

• CCS, Process calculusEx: C = in(x)C1;C1 = in(y)C2;C2 = ¯out(x)C1;C1 = ¯out(y)C

• π-calculus• Stream-based interactive components

(Broy et. al http://www4.informatik.tu-muenchen.de/proj/focus/Literature.html)

http://http://www.iiitb.ac.in/http://www4.informatik.tu-muenchen.de/proj/focus/Literature.htmlhttp://www4.informatik.tu-muenchen.de/proj/focus/Literature.html

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(PERCEIVED) SHORTCOMINGS WITH CURRENT MODELS

• Channels are statically defined and the number of channels isfixed.

• Channel behaviour is also fixed.• Models employ an “operational” view of channel behaviour

specifying exact tokens of exchange taking place through thechannels.


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“I NTERACTION SCHEMA” MODEL

• System consists of an unbounded but finite number of channels

• Each channel is concerned with only its view of the global, persistent,shared state

• No channel has the complete global state. The global state is manifested bycombining all the different local views using a set of combination policies

• The set of combination policies is called theinteraction schema.


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THE MULTI -CHANNEL SERVICE OBJECT

The multi-channel service object has the following components:

• S – a set of states or “starting points”

• ψ – a set ofconstraintsacross states inS

Instances of a service object are called “channels”. At any point in time, achannel can be in any of the states ofS. If channelx is in states, it is said to“inhabit” s.

Channel inhabitations change as it interacts with its environment.

Each change in state is a computation – or an ACID transaction.


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MULTI -CHANNEL SERVICE OBJECT

The “condition” part of each states forms the “entry condition” for a channel toenters.

The entry condition is a condition on the interaction history of a chan-nel before it arrived at the present state. (Ex. In order to arrive at stateinsurance-pending the incumbent channel should have visited stateadmission-over )

A channel not satisfying the entry condition rolls back to wherever it came from.


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A channel is an instance of a service object. Any channelx has the followingdescriptors:

• state(x) returns the current state thatx is inhabiting

• hist(x) ∈ S∗ returns the channel’s trajectory in the state space

• in(x) returns a handle to the input data stream for channelx

• out(x) returns a handle to the output data stream for channelx


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Constraints in a service object are of the form:s1 ∧ s2 . . . ∧ sn →M [s].

It is read as “if there are channels inhabitings1, s2, . . . sn, then states gets amodalityM .” HereM is one of the following:

• O[s] : it is obligatedfor a channel to inhabits. Until the antecedent holds,all channels in the precedent of the rule areblocked.

• P [s] : it is permittedfor a channel to inhabits

• F [s] : it is forbiddenfor any channel to inhabits. If there are any channelsin s when the rule holds, then all of them areblocked.

When a channel isblocked, its input and output streams are cut off and any out-

put it generates are buffered. All method calls to the channel are also disabled.


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When two or more constraints hold on a state, their net effect is the logical“and” of all the incoming constraints. When a constraint ceases to hold, the seteffect is the logical “negation” of the constraint.

Following axioms define logical operators on normative constructs:

1. O ∧ P ⇒ O

2. P ∧ F ⇒ F

3. F [O ∧ F ]

4. ¬O ⇒ P

5. ¬P ⇒ F

6. ¬F ⇒ P

The third axiom is the “crash condition” when a state is obligated and forbidden

at the same time, an exception is raised and the later constraint that was fired is

killed.


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THE INTERACTION SCHEMA

The interaction schema is simply a collection of service objectsand constraints across service objects.

The interaction schema itself is work in progress and we shall notbe discussing it further here..


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CONCLUSIONS

• Designing interactive systems is really about designing “open” systems

• Open systems have onlypartial controlover their own dynamics

• Interaction = computation + persistent state + channel sensitivity

• Open systems necessarily have to be designed in such a way so as to be ableto include new “starting points” of computation dynamically

Philosophical question:

Is the universe inductive (minimalistic) or coinductive (maximalistic)?

international workshop on software design and architecture...

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