Lec16_Finite_State_Automata

Lec16_Finite_State_Automata - Discrete Structures TDS1191 -...

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[Lecture 16][Finite State Automata] Discrete Structures 1 Discrete Structures TDS1191 - Lecture 16 - Finite State Automata
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[Lecture 16][Finite State Automata] Discrete Structures 2 Finite State Machine Introduction: The usual combinatorial circuit has the characteristic that its output depends solely on the present input. In other words, the circuit does not exhibit memory. There exist more powerful circuits whose behavior depends not only on the present input but also on the past inputs. Such circuits are called sequential circuits. Finite-state machines are abstract models of machine with a limited memory . Finite automaton is a special type of finite- state machines.
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[Lecture 16][Finite State Automata] Discrete Structures 3 Finite State Machine with Output Definition : A finite-state machine M consists of A finite set S of states A finite set I of input symbols A finite set O of output symbols A next-state function f : S × I S An output function g : S × I O , and An initial state s 0 S . We write M = ( S, I, O, f, g, s 0 ).
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[Lecture 16][Finite State Automata] Discrete Structures 4 Finite State Machine with Output Definition : Let M = (S, I, O, f, g, s 0 ) be a finite-state machine. The transition diagram/state diagram of M is a digraph G whose vertices are the members of S . An arrow designates the initial state s 0 . A directed edge ( s 1 , s 2 ) exists in G if there exists an input i with f (s 1 , i ) = s 2 . In this case, if g ( s 1 , i ) = 0, the edge ( s 1 , s 2 ) is labeled i/0 .
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[Lecture 16][Finite State Automata] Discrete Structures 5 Finite State Machine with Output Example : Let I ={ a , b }, O = {0, 1}, S = { σ 0 , 1 } and s 0 = 0 . Define f : S × I S and g : S × I O as in the following state table : continue
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[Lecture 16][Finite State Automata] Discrete Structures 6 Finite State Machine with Output Example (Continue): The foregoing state table is interpreted as follows: A transition diagram may as well describe the next-state function and the output function:
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[Lecture 16][Finite State Automata] Discrete Structures 7 Finite State Machine with Output Definition : Let M = ( S, I, O, f, g, s 0 ) be a finite-state machine. An input string for M is a string over I . The string y 1 …y n is the output string for M corresponding to the input string
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Lec16_Finite_State_Automata - Discrete Structures TDS1191 -...

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