ENMA 6010
© 2010 Mark Polczynski
All rights reserved
Reference: Wikipedia – State Transition Diagrams
ENMA 6010: State Transition Diagrams 1

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.
ENMA 6010: State Transition Diagrams 2

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.
ENMA 6010: State Transition Diagrams 3

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?
ENMA 6010: State Transition Diagrams 4

Process flow diagram
Control flow
Control function
State transition diagram
Entity relationship diagram
ENMA 6010: State Transition Diagrams 5

• 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.
ENMA 6010: State Transition Diagrams 6

• 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…
ENMA 6010: State Transition Diagrams 7

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., heat ing oven, mix ing ingredients, accelerat ing engine,
• Waiting for something to happen – Wait ing for user to enter password, wait ing for sensor reading.
Transition:
(Virtually) instantaneous change in state (behavior).
ENMA 6010: State Transition Diagrams 8

Here’s a simple example STD for a washing machine.
State
Transition
Condition
Action
ENMA 6010: State Transition Diagrams 9

A condition is typically some kind of event , e.g.:
• Signal
• Arrival of an object (data/material),
• Etc…
An action is the appropriate output or response to the event, e.g.:
• Signal or message
• Transfer of an object,
• Calculation,
• Etc…
Condition
Action
ENMA 6010: State Transition Diagrams 10

Here’s a simplified data flow diagram for our wash machine, which shows the three primary functions and associated material flows:
State transition diagram
How does this relate to our state transition diagram?
ENMA 6010: State Transition Diagrams 11

Control lines in DFD are associated with conditions and actions in STD
1-bit on/off signals
Timer
ENMA 6010: State Transition Diagrams 12

Similarly…
• The DFD shows flow of entities for Make Lunch
• The STD shows timing for Make Lunch
ENMA 6010: State Transition Diagrams 13

This is pretty boring, isn’t it?
Couldn’t we just write this down as a sequence of text statements?
Start
Do until wash cycle complete
Wash clothes
Do until rinse cycle complete
Rinse cloths
Do until spin cycle complete
Spin-dry clothes
End
ENMA 6010: State Transition Diagrams 14

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.
ENMA 6010: State Transition Diagrams 15

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?
ENMA 6010: State Transition Diagrams 16

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.
Condition X =
External event at terminator
Action Y =
Response to terminator
External
Terminator
State
Object 1
Condition X
Action Y
Object 2
Context
Diagram
ENMA 6010: State Transition Diagrams 17

• 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.
ENMA 6010: State Transition Diagrams 18

PowerPoint waiting for user to select function
Several possible state transitions
Condition: Select “File”
Action: Open File dialog box
PPT waiting for “File” function selection
Several possible state transitions
ENMA 6010: State Transition Diagrams 19

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…
ENMA 6010: State Transition Diagrams 20

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?
ENMA 6010: State Transition Diagrams 21

A state with no transition arrows out is the system’s end state
A system can have multiple end states
ENMA 6010: State Transition Diagrams
But…
22

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…
ENMA 6010: State Transition Diagrams 23

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.
ENMA 6010: State Transition Diagrams 24

Thug insults Dirty Harry
“Make my day!”
Waiting for trigger pulled
Guard
Trigger pulled & safety on
Bullet fired disabled
Trigger pulled & safety off
Bullet fired
Captain arrives
Gun holstered
ENMA 6010: State Transition Diagrams
Common example of the use of a state transition guard
25

Returning to our simplified washing machine…
Rinse signal
Start rinse cycle
Timer
Idle
Wash signal
Star wash cycle
Washing
Guard
Wash cycle complete
Start rinse cycle
Rinsing
Spin-dry cycle
Complete
Sound buzzer
Door open
Disable spin-dry cycle
Rinse cycle complete
Start spin-dry cycle
Can’t start the spin cycle while the door is open.
Spin-drying
ENMA 6010: State Transition Diagrams 26

• 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…
ENMA 6010: State Transition Diagrams 27

Just as for functions in data flow diagrams, states can be broken into sub-states.
ENMA 6010: State Transition Diagrams 28

• 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 lunch
ENMA 6010: State Transition Diagrams 29

• 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.
ENMA 6010: State Transition Diagrams 30

PowerPoint waiting for user to select function
Several possible state transitions
PPT waiting for “File” function selection
Several possible state transitions
Here’s another difference between logical and physical models–
Logical model condition:
Select “File”
Implementation independent
Physical model condition:
Left click on “File”
Or keyboard Alt-F
Implementation dependent
ENMA 6010: State Transition Diagrams 31

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.
ENMA 6010: State Transition Diagrams 32

For 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 X
Condition X
Action X
“Gene”
Add link when you find Action X which produced Condition Y.
State Y
Condition Y
Action Y
ENMA 6010: State Transition Diagrams 33

This process works pretty well for having at team jointly converge to a state transition diagram.
Here, individuals write individual condition/action/state chromosomes on postit 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.
ENMA 6010: State Transition Diagrams 34

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.
ENMA 6010: State Transition Diagrams 35

Enter
Identify
States
List all events that occur in the system
For each event, identify the corresponding action
Build
Diagram
Compare all eventaction-state sets
Link states with actions
For each event-action pair, identify a unique
“following” state
Eliminate duplicate states
Put the event-actionstate sets on selfstick notes
Identify missing states
Test
Model
Walk through system operation using the model
Review and Revise
Exit
Process Flow Diagram for
State Transition
Diagramming
No
Model accurate?
Yes
Use the model
ENMA 6010: State Transition Diagrams 36

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.
From The state transition matrix can help.
To
State 1
State 2
State 3 etc…
Condition
Action
Condition
Action
ENMA 6010: State Transition Diagrams 37

From
Do this first to define desired operation.
Check blank cells – have we covered all possible desired transitions?
To
Idle
Wash signal
Washing
Start wash cycle
Rinsing
Rinse signal Wash cycle complete
Start rinse cycle Start rinse cycle
Spin-
Drying
Rinse cycle complete
Start Spin-dry cycle
ENMA 6010: State Transition Diagrams
Spin-dry cycle complete
Sound buzzer
38

Rinse signal
Start rinse cycle
Idle
Wash signal
Star wash cycle
Washing
Wash cycle complete
Start rinse cycle
Rinsing
Spin-dry cycle
Complete
Sound buzzer
Door open
Disable spin-dry cycle
Rinse cycle complete
Start spin-dry cycle
Spin-drying
To
Idle
Do this next to incorporate guards.
Washing
Rinsing
Spin-
Drying
From
ENMA 6010: State Transition Diagrams
Door open
Disable spin-dry cycle
39

Idle
Start signal
Star wash cycle
Stop signal
Stop washing
Washing
Wash cycle complete
Start rinse cycle
Stop signal
Stop rinsing
Rinsing
Stop signal
Stop spin-drying
Rinse cycle complete
Start spin-dry cycle
Spin-drying
Spin-dry cycle
Complete
Sound buzzer
To
Idle
Finally, do this to cover all the possible exceptions to the normal operating sequence.
Washing
Rinsing
Spin-
Drying
From
Stop signal Stop signal Stop signal
Stop wash cycle Stip rinse cycle Stop spin-dry cycle
ENMA 6010: State Transition Diagrams 40

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).
Start
ENMA 6010: State Transition Diagrams
End
41

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…
ENMA 6010: State Transition Diagrams 42

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
ENMA 6010: State Transition Diagrams 43

Customer
STD
This describes the states that the customer is in vs. the call center system states.
ENMA 6010: State Transition Diagrams 44

Customer’s emotional state
STD
ENMA 6010: State Transition Diagrams 45

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?
ENMA 6010: State Transition Diagrams 46

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.
ENMA 6010: State Transition Diagrams 47

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?
ENMA 6010: State Transition Diagrams 48

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?
ENMA 6010: State Transition Diagrams 49

Process flow diagram
Control flow
Control function
State transition diagram
Entity relationship diagram
ENMA 6010: State Transition Diagrams 50