Finite State Machines State Transition Diagrams

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Finite State Machines(State Transition Diagrams)

• Explain the FSM concept
• Represent an FSM
• as a diagram as a table
• Discuss uses of FSMs
• Create an FSM from a description

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What is a finite state machine?

• A system with
• A limited number of internal "states" (modes)
• These control its response to an input.
• In different states it may react differently to
  an input
• Describe an FSM by defining for each state
• the response (action) and next state (state
  transition) generated by an input (event
• Representing an FSM
• State transition diagram
• Table

3
Coffee Machine Specification

• Behaviour
• Accepts 5, 10, 20p coins
• Coffee costs 25p
• Is this enough for a specification?

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Diagram Representation
20p/Issue
Total0
Total0
Total0
5, 10, 20p/Issue
20p
10p
5p
10, 20p/Issue
20p/Issue
Total20
Total15
Total10
Total5
Total20
Total10
5p
5p
5p
10p
10p
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Table Representation
Current Event
Action
Current State
Next State
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Why use an FSM?

• Clear description of behaviour
• Diagram
• Can be easier to understand than text
• Simple clear semantics (meaning)
• Allow checking for desirable properties
• E.g. deadlocks
• System trapped in a group of states
• See reasoning about protocol in tutorial

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Applications of FSM

• Digital logic
• Specifying data communication protocols
• Specifying user dialogues
• Defining class behaviour in UML
• But
• All computers are finite state machines but
  because of large amount of memory usually dont
  treat as finite state machines
• Too complex

A useful technique but can be overwhelmed by
complexity
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FSM User Interfaces

• Used to define interaction
• States
• Permitted user actions (FSM events)
• Responses (FSM actions)
• Identical input may give different outputs
• E.g. Word
• Close empty file, modified file, saved file
• Typing insert/overtype, Caps lock/shift
• Design FSM to represent these situations

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Word
New
Close
No file
Empty file
New/ Create file
No
New/ Create file
Close
type
Clean file
Yes/ Save
Save
type
Dirty file
Displaying Save Dialogue
Close/ Display Dialogue

• Is it correct?
• Is it complete?

Cancel
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Calculator

• Is it complete?
• Is it correct?

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Workflow Applications

• An employee creates a purchase order.
• The employee can modify and save this draft order
  as many times as required.
• The employee can submit an order to a manager for
  approval or rejection.
• If the manager rejects it, the purchase order
  returns to the draft state.
• Approved or draft items can be deleted.
• Items waiting for approval cant be deleted.

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Workflow Applications
reject
Draft
Awaiting Approval
approve
create

submit
modify
delete
Approved
delete
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FSM Languages Identifiers
?
non-letter
other
any
letter
?
?
letter
digit

• Is this correct?
• How would you allow _

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FSM Languages Numbers
Integer
digit
,-
?
digit
digit

• This uses a different convention for errors
• Describe this convention
• Is this definition of integers correct?
• Can you define floating point numbers?

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FSM Languages

• FSM can recognise sets of words
• e.g. identifiers, numbers, filenames (.txt)
• But not every possible set
• e.g. cant recognise matching brackets
• Why not?
• Uses
• Editor (global search and replace)
• g/ / /p replace two or more spaces by a space
• Pattern matching in JavaScript
• Unix utilities
• GREP find files containing a pattern
• LEX generate a recogniser

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Reasoning about FSM
Validated
PIN
Not validated
Remove card / deliver cash
Remove card
Card inserted
Receipt not wanted
Want receipt / Print receipt

• Can a receipt be given with no valid PIN?
• Can the system be stuck in a small set of states?
• Is the specification complete?

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Problems with FSM

• Complexity
• They can have many states and transitions
• Allow variables and conditions
• Modify the notation
• Allow nested states
• Allow actions that occur when a state is entered
  or left
• Limited expressiveness
• Cant define some behaviours
• E.g. correct matching of brackets
• Imagine you have 10 states in your FSM
• Input 10 ( - system goes through all states why?
• Input a ( - must go into an existing state so?

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Summary

• FSM can model many systems
• Digital hardware
• User interface
• Communication Protocols
• Systems with modes
• Clear specification
• Allow reasoning
• Checking consistency completeness
• Complexity theoretical limitations