Introduction to Finite State Machine (FSM)

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Introduction to Finite State Machine (FSM)

• Csci562

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Objectives

• Automata Based specification
• Finite State Machine
• Statecharts
• Petri Nets

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FSM

• Key characteristics of FSM
• Focus is on control
• Appropriate for specifying systems having finite
  set of states
• Used to specify a system with limited states
  (e.g. ,lexical analyzers)
• Key problem
• State Explosion Problem (SEP)
• A variety of models have been proposed to
  overcome SEP

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Simple DFA Lexical analyzer
a d
a
A B
A
B
a
B B B
d
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Simulating DFA

• Input an input string X terminated by eof
• Output
• Yes if M accepts string x,
• No otherwise

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FSM Simulation Algorithm
s S0 c getnextchar() While c? eof do s
move(s,c) cgetnextchar End If s ?F then
return yes Else return no
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Nondeterministic FA (NFA)

• NFA
• Differs from deterministic model
• For any given state and input symbol, there may
  exist more than one transition

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example

• FA for (ab)abb

b
b
0
1
3
2
a
b
a
Possible paths lt0, 0, 1,2,3gt, lt0,0,0,0,0gt
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Example A chocolate Vending Machine (CVM)

• CVM will dispense a chocolate bar for 11 cents.
• The requirements for machine are
• Accepts 1, 10 cents
• Gives no changes
• Refunds all coins if wrong amount (too little or
  too much) is given
• Cannot accepts more than two coins

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