enma 6010: state transition diagrams1 enma 6010 state transition diagrams modeling time-dependent...

ENMA 6010: State Transition Diagrams 1

ENMA 6010

State Transition Diagrams

Modeling Time-Dependent Behavior

Reference: Wikipedia – State Transition Diagrams

© 2010 Mark PolczynskiAll rights reserved

http://www.yourdon.com/strucanalysis/chapters/ch13.html


Characteristics of Good Models

1.Graphical, with support for detailed text descriptions: Picture is worth a thousand words picture links to a thousand words.

2.Top-down partitionable: Globe Continents Countries

3.Minimally redundant: Make changes in just one place in the model.

4.Transparent: Requires no expertise in model building to understand the model.


Goals of System Modeling:

1.To focus on important system features while downplaying less important features,

2.To discuss changes and corrections to the user’s requirements at low cost and with minimal risk,

3.To verify that we understand the user’s environment,

4.To verify that we have documented our understanding in a way that would allow others to construct/maintain the system.


We will be studying four related modeling approaches:

• Data flow diagram – system function

• State transition diagrams – time dependent behavior

• Entity relationship diagram – stored data/material

• Process flow diagrams – actions and decisions

How does this fit?


Statetransitiondiagram

Entity relationship diagram

Process flow diagram

Controlflow

Control function


Control Function

•The control function coordinates the activities of the other DFD functions.

•Control function inputs and outputs are 1-bit on/off yes/no signals.

•No data/materials flowing on control lines!

•These signals “wake up” other DFD functions when the function needs to transform inputs to outputs.

•These could be expected or unexpected conditions.

•Typically there is only one control function for a particular data flow diagram.


STD vs. DFD

•The state transition diagram goes inside the control function.

•The control function inputs and outputs connect to the state transition diagram.

•The STD defines how the DFD functions (bubbles) get turned on and off.

•Thus, the state transition diagram controls system sequencing and timing.

Let’s see how this works…


State Transition Diagrams

State:Some behavior of a system that is observable and that lasts for some period of time.

A state is when a system is:

• Doing something – e.g., heating oven, mixing ingredients, accelerating engine,

• Waiting for something to happen – Waiting for user to enter password, waiting for sensor reading.

Transition: (Virtually) instantaneous change in state (behavior).


Here’s a simple example STD for a washing machine.

State

Transition

Condition

Action


A condition is typically some kind of event, e.g.:•Signal•Arrival of an object (data/material),•Etc…

Condition

Action

An action is the appropriate output or response to the event, e.g.:•Signal or message•Transfer of an object,•Calculation,•Etc…


Here’s a simplified data flow diagram for our wash machine,which shows the three primary functions and associated material flows:

How does this relate to our state transition diagram?



Control lines in DFD are associated with conditions and actions in STD

1-bit on/off signals

1-bit on/off signals

Timer


Similarly…

•The DFD shows flow of entities for Make Lunch

•The STD shows timing for Make Lunch


This is pretty boring, isn’t it?

Couldn’t we just write this down as a sequence of text statements?

StartDo until wash cycle complete

Wash clothesDo until rinse cycle complete

Rinse clothsDo until spin cycle complete

Spin-dry clothesEnd


Here’s a more interesting (simplified) diagram which shows exception handling.

Text descriptions start getting messy when you have to account for every possible if-then-else exception to normal operation.


Here’s an even more interesting example.

It is now perfectly clear that you:

•Can go right to rinsing without washing, but..

•Can never go to spin-drying without rinsing.

So, what would I use such a modeling technique for?


State Transition Diagram vs. DFD Context Diagram

For DFDs, we used the context diagram to show how the system interacts with the external world (terminators).

For STDs, a condition can be an event occurring in the environment external to the system being modeled,

And actions can be responses sent back to the external environment.

State

Condition X =External event at terminator

Action Y =Response to terminator

ExternalTerminator

ContextDiagram

Object 1

Object 2

Action Y

Condition X


State Transition Diagram Use• State transition diagrams have bee used for a long time to model

real-time systems such as:

• Process control,

• Telephone switching systems,

• Data acquisition systems,

• Military command and control systems.

• They are also quite useful in modeling “object oriented systems”such as those produced by Visual Basic.

• These are software program that basically sit there waiting until you initiate an event such as clicking an icon or hitting the “Enter” key.


Condition: Select “File”Action: Open File dialog box

PowerPoint waiting for user to select function

PPT waiting for “File” function selection

Several possiblestate transitions



Building State Transition Models

The literature and the references for this course provide details on rules and processes for building good state transition models.

We will not cover these details here, but we will touch on some key points in the following slides…


A transition arrow without an originating state is the

system’s start state

A system is not required to have a specified start state, but most do.

For example, does your computer always start in a pre-defined state when power is applied?

Or does it power up running PPT some days, and Outlook others?


A state with no transition arrows out is the system’s

end state

A system can havemultiple end states

But…


Systems typically do not have end states. The end state is essentially “dead”, since

you can’t ever get back to any other state.

Except if you are a cruise missile…


Guards

So far, we have seen the use of states, transitions, events, and actions.

A guard is a True/False statement that enables a transition to occur.

In this example of editing a PowerPoint presentation…

no object in the ppt slide has been selected…

so the Cut, Copy, and Clear functions are disabled.

This is because a guard has detected that “object selected” is “false”, so transitions to these states are not allowed.


Waiting for trigger pulled

Trigger pulled & safety on

Bullet fired disabled

Trigger pulled & safety off

Bullet fired

Thug insults Dirty Harry“Make my day!”

Guard

Captain arrivesGun holstered

Common exampleof the use of a

state transition guard

Common exampleof the use of a

state transition guard

Idle

Washing

Rinsing

Spin-drying

Rinse cycle completeStart spin-dry cycle

Wash cycle completeStart rinse cycle

Wash signalStar wash cycle

Spin-dry cycle Complete

Sound buzzer

Rinse signalStart rinse cycle

Door openDisable spin-dry cycle


Returning to our simplifiedwashing machine…

Guard

Can’t start the spin cycle while the door is open.

Can’t start the spin cycle while the door is open.

Timer


Top-Down Partitionable Modeling

•Recall that STDs are inside of the control functions on DFDs.

•Now, DFDs can be decomposed into levels, and STDs follow the DFDs,so STDs are naturally decomposable.

Furthermore!

Sometimes it can help clarify things if you decompose an STD within a DFD…


Top-Down Modeling:

Just as for functions in data flow diagrams,states can be broken into sub-states.


STD Logical Models vs. Physical Models

• For data flow diagrams, we distinguished between logical models and physical models (essential vs. environmental models).

• For DFDs, the major difference is usually the appearance of “implementation stores” which buffer objects (data/materials).

• We use these to store objects while we are “waiting for” something to happen.

• A similar situation holds for STDs.

Waiting for lunchWaiting

for lunch


Logical Models vs. Physical Models

• In the logical/essential world, state transitions are virtually instantaneous.

• But in the real world, transitions may actually take some time,just like DFD functions take time.

• This may cause “Waiting for transition to complete” states to be added to the physical/environmental model used used for actual system implementation.

• This is just like adding implementation stores to DFDs.


Here’s another difference between logical and physical models–

Logical model condition: Select “File”

Physical model condition: Left click on “File” Or keyboard Alt-F

PowerPoint waiting for user to select function

PPT waiting for “File” function selection



Implementationindependent

Implementationdependent


Building a State Transition Diagram

Here is one approach:

1. Identify an initial state and walk through the sequence of states.

2. Look for all possible state transitions (branches) as each state is identified.

For the second approach, states can be identified through a systematic process:

1. List all of the conditions that the system takes,

2. Identify all of the actions that result from each condition.

3. Identify the state that follows each condition/action pair: what is the system waiting for after the action takes place?

4. Look for additional condition/action pairs not initially identified.


Building a State Transition DiagramFor the second approach, you have a bunch of condition/action/state “genes”.

Now, you need to link all of the genes together into a chromosome:For each state, what condition(s)/event(s) is the system waiting for?What chromosome(s) provide the event?

State Y

Condition YAction Y

State X

Condition XAction X

Add link when you find Action X which produced Condition Y.

“Gene”


Building a State Transition DiagramThis process works pretty well for having at team jointly converge to a state

transition diagram.

Here, individuals write individual condition/action/state chromosomes on post-it notes.

Then, the team compares individual chromosomes, modifying, combining and eliminating as needed.

Chromosomes can then be assembled into a diagram. Do this by randomly selecting one chromosome, and then finding the chromosomes with the conditions that the chromosome state is waiting for.

Repeat this for al the chromosomes you just added to the diagram, and iterate until all the chromosomes are used up.

It can be tempting for individuals to assemble their chromosomes into diagrams before comparing with the team, but the team should reach consensus on chromosomes before assembling the diagram.


Building a State Transition Diagram

After you have constructed the diagram, check the following:

1. Do you have a start and one or more end states (if needed)?

2. Can you transition into all states except the start state?

3. Can you exit all states except end states?

4. Are there any other conditions not covered?

5. Are there any other actions not covered?

If possible, check your diagram by doing a live process walk-through.


List all eventsthat occur in the

system

For each event, identify the

corresponding action

Put the event-action-state sets on self-

stick notes

For each event-action pair, identify a unique

“following” state

Link states with actions

Compare all event-action-state sets

Eliminate duplicate states

Walk through system operation using the

model

Model accurate?

Use themodel

Identifymissingstates

Enter ExitBuildDiagram

IdentifyStates

Reviewand Revise

TestModel

Yes

No

Process Flow Diagram for State Transition Diagramming


State Transition Matrix

As with DFDs and ERDs, things can get pretty messy.

Plus, it’s nice to have a systematic way to check for consistency,

And also to identify the myriad exception/unexpected situations.

The state transition matrixcan help.

From

Stat

e 1

Stat

e 2

Stat

e 3

etc…

ToState 1

State 2Condition

Action

State 3Condition

Action

etc…


From

Idle

Was

hing

Rins

ing

Spin

-Dry

ing

ToIdle

Spin-dry cycle complete

Sound buzzer

WashingWash signal

Start wash cycle

RinsingRinse signal Wash cycle

completeStart rinse cycle Start rinse cycle

Spin-Drying

Rinse cycle complete

Start Spin-dry cycle

1. Primary State Transitions

Do this first to define desired operation.

Check blank cells – have we covered all possible desired transitions?


2. Guards

Do this next to incorporate guards.

From

Idle

Was

hing

Rins

ing

Spin

-Dry

ing

ToIdle

Washing

Rinsing

Spin-Drying

Door open

Disable spin-dry cycle

Idle

Washing

Rinsing

Spin-drying



Wash signalStar wash cycle


Sound buzzer

Rinse signalStart rinse cycle

Door openDisable spin-dry cycle


Idle

Washing

Rinsing

Spin-drying



Start signalStar wash cycle


Sound buzzer

Stop signalStop washing

Stop signalStop rinsing

Stop signalStop spin-drying

3. Exceptions

From

Idle

Was

hing

Rins

ing

Spin

-Dry

ing

ToIdle

Stop signal Stop signal Stop signal

Stop wash cycle Stip rinse cycle Stop spin-dry cycle

Washing

Rinsing

Spin-Drying

Finally, do this to cover all the possible exceptions to the normal operating sequence.


State Transition Diagram Example

Here is part of a STD for a calculator, highlighting the function of the Clear and Off buttons, using UML (unified modeling language) notation (see: http://en.wikipedia.org/wiki/UML_state_machine).

StartStart

EndEnd

http://upload.wikimedia.org/wikipedia/en/2/2f/UML_state_machine_Fig2a.png


State Transition Diagram Example

Here is an interesting example of a state transition diagram:

““The Emotional State-Transition Diagram”

http://syque.com/articles/state-transition/state-transition.htm

The first diagram shows what happens when a customer calls in to a call center with a problem…

http://syque.com/articles/state-transition/state-transition.htm


Note: This is an “expected” sequence. The “unexpected” events and transitions have not been considered, e.g., customer dials wrong number.

Call center system STD


CustomerSTD

This describes the states that the customer is invs. the call center system states.


Customer’s emotional state

STD


Finally:

As mentioned, a state is when a system is:

• Doing something - Heating oven, mixing ingredients, accelerating engine,

• Waiting for something to happen – Waiting for user to enter password, waiting for sensor reading.

Well, waiting for something to happen is just a waste of time,

So state transition diagrams can be helpful in identifying and minimizing or eliminating time-wasting states.

Just like data flow diagrams were useful in identifying and minimizing or eliminating inventory and work-in-process.

You can do this by comparing logical/essential models with physical/environmental implementation models.

Do you really need to wait for some thing to happen?


Characteristics of Good Models

1.Graphical, with support for detailed text descriptions: Picture is worth a thousand words picture links to a thousand words.

2.Top-down partitionable: Globe Continents Countries

3.Minimally redundant: Make changes in just one place in the model.

4.Transparent: Requires no expertise in model building to understand the model.


Goals of System Modeling:

1.To focus on important system features while downplaying less important features,

2.To discuss changes and corrections to the user’s requirements at low cost and with minimal risk,

3.To verify that we understand the user’s environment,

4.To verify that we have documented our understanding in a way that would allow others to construct/maintain the system.

What’s next?


We will be studying five modeling approaches:

• Data flow diagram – system function

• State transition diagrams – time dependent behavior

• Entity relationship diagram – stored data/material

• Process flow diagrams – actions and decisions

How does this fit?



Entity relationship diagram

Process flow diagram

Controlflow

Control function

enma 6010: state transition diagrams1 enma 6010 state transition diagrams modeling time-dependent...

Documents

state transition diagrams10

state transition diagrams4

state behavior

state transition diagrams7

control function inputs

control lines

particular data flow

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