1. Finite State Machines Part I
State Based Computing

2. State-based Reasoning
The state of a computation is
all the internal information needed to take the next step in the computation
0 NEWx -> S 1
previous state
next state
external input data
literal next step
(action)

3. Picobot == state machine
each oval represents a different robot state
Semantic action
***x/
move S
x***/move N
N***
state pattern -> move new state
start
here
state 0
state 1
0 x*** -> N 0
0 N*** -> X 1
1 ***x -> S 1
1 ***S -> X 0
the "go North" state
the "go South"
state
***S
transitions move from state to state

4. All computation can be considered a deliberate sequence of state-changes
bits before
bits after

5. A model of computation: FSM
FSM or Finite State Machine
Example: 1 s0 s1 1
start state
transitions
accepting states
Don't give the answer of what each state means yet… two slides away!
“input funnel”
“where to go”
double circled
labeled by input !
How it runs:
100101
input sequence
read left-to-right

6. Parts of a Finite State Machine (FSM)
1. Must have a finite number of states, i.e., can't be an infinite number. Drawn as circles with label. 2. Must have one starting state designated by 3. Have a non empty subset of the states called final or accepting states designated by double circles. 4. Have transitions of how to change from one state to another state. Drawn as arrows labeled with the input character read. 5. Rule of acceptance: If on reading the last input character the FSM is in a final state, the FSM accepts, otherwise rejects. s0 s1
0,1 s0 s1
FSM accepts all binary strings with at least one 1. 1

7. 0010111 FSM: Finite state machine State 1 State 0 transition on 0
Oh, how I wish we could discuss regex!
State 0 – Even number of 1s seen so far
State 1 – Odd 1s
This accepts sequences of any string with an odd number of 1s
another input sequence
What does each state MEAN ?
What does this FSM do overall?
always left-to-right

8. How to Program a FSM? "Count the words in a file" example
FSMs great for design of character processing problems
Translation to Python program mechanical!

9. How to Program a FSM?
state = 'WS' # start state for FSM words = 0 # action done at start of FSM for line in file1: for ch in line: # FSM-For each character read, depending on character read #and current state, change to new state and do any actions. if state == 'WS': if isWhitespace(ch): state = 'WS' else: state = 'WORD' words += 1 # action elif state == 'WORD': print('Should not be here! Must be programming error!') # End of FSM