Finite state machines. Finite State Machines (FSMs) Widely used specification technique Used to specify system behavior in response to events Both output

Finite state machines

Finite State Machines(FSMs)

• Widely used specification technique• Used to specify system behavior in

response to events• Both output and next state can be

determined solely on the basis of understanding the current state and the event that caused the transition

• H/W engineers have been using FSM for years

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Same stimulus event

Different response

State Machines• Models how a system responds

differently to events over time

State Machines

• Models how a system responds differently to events over time

button switch

States

ON OFF

States

ON OFF

Press

Press

Finite State Machines• State

– the memory of previous events• Events

– inputs to a system• Actions

– output in some form•mechanical, electrical or software

event

Finite State Machines• State

– the memory of previous events• Events

– inputs to a system• Actions

– output in some form•mechanical, electrical or software

event

Coke Machine• Events

– coin insertion• Actions

– coke delivery– coins returned

• State– the memory of how much money

has been deposited

FSM Diagram

State 1 State 2Event-1

Action-k

FSM

State 1 State 2Event-1

Action-k

Event-1

Not all state transitions have actions associated with them

ScenarioQuarters Only, 75 cents• Customer

– enter quarter• Customer

– enter quarter• Customer

– enter quarter• Coke Machine

– deliver coke

Enumerate Events & Actions

Events:E1: Deposit 25 cents

Actions:A1: Deliver coke

Define States

A B

C

Start State

E1

E1E1/A1

States:A: No moneyB: 25 cents enteredC: 50 cents entered

Events:E1: Deposit 25 cents

Actions:A1: Deliver coke

State Transition TableCurrentState

EventE1

A B

B C

C A/deliver coke

Coke Machine Scenario 2Coin Return

• Customer– enter quarter

• Customer– enter quarter

• Customer– press coin return (CR)

• Coke Machine– return coins

Enumerate Events & Actions

Events:E1: Deposit 25 centsE2: Coin Return (CR)Actions:A1: Deliver cokeA2: Return coins

Define States

A B

C

Start State

E1

E1E1/A1



E2/A2

Define States

A B

C

Start State

E1

E1E1/A1



E2/A2

E2/A2

Transition Table• State E1 E2• A B• B C A/coin

return• C A/coke A/coin

return

Transition TableTransition Table

State E1 E2 A B B C A/coin return C A/coke A/coin return

No BlanksAllowed !!

Transition Table

• State E1 E2• A B A• B C A/coin return• C A/coke A/coin return

Telephone System FSMLocal 4-digit exchange

Eventsd: digit dialedh: hang up

Actionsc1: connect to caller


A B C D Ed d d d/c1

StatesA: startB: 1 digit dialedC: 2 digits dialedD: 3 digits dialedE: call in progress




A B C D Ed d d d/c1

h





A B C D Ed d d d/c1

h




Problems with FSMs• The state explosion problem• Confusing when too many states• Requirements:

– “in all airborne states, when the yellow handle is pulled, the seat will be ejected”•maps event to large collection of states

– “when the selection button is pressed, enter the selected mode”• implies a clustering or grouping of states

Harel’s State Charts• Allows grouping or clustering of states

ab

cb

c

A

C

B

a

b

c

c

A

C

B

D

Clustering into new superstate D - reallyan abstraction. To be in D really means to be ineither A or C

Coke Machine

E

D F10

A

B

5

10C

5

5

10/coke

5/coke5

Coke Machine

A

B E

D F5

10C

5

10 5

10/coke

5/coke5

CR

CR

CR ouch!

No Money

(A)

Money Entered

No Money

(A)

Money Entered

5

10

CR

No Money

(A)

Money Entered

5

10

CR

B

5 10C5

Documents

Finite state machines. Finite State Machines (FSMs) Widely used specification technique Used to specify system behavior in response to events Both output