2 it plays an important role in complier design 3 to

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2. It plays an important role in complier design. 3. To prove the correctness of the program automata theory is used. 4. In switching theory and design and analysis of digital circuits automata theory is applied. 5. It deals with the design finite state machines. V1 V2 V4 V3 V1 V2 V4 V3
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III Year V Semester CSE CS2303 Theory of Computation Adhiparasakthi College of Engg., G.B. Nagar, Kalavai Page 3 of 20 9. Define Finite Automation. A finite automata is a collection of 5 tuples (Q, Σ. δ , q 0 , F ) where Q is a finite set of states, which is non empty. Σ is a input alphabet, indicates input set. δ is a transition function or a function defined for going to next state. q 0 is an initial state (q 0 in Q) F is a set of final states. Two types : Deterministic Finite Automation (DFA) Non-Deterministic Finite Automation. (NFA) 10. Define Deterministic Finite Automation. - The finite automata is called DFA if there is only one path for a specific input from current state to next state. - A finite automata is a collection of 5 tuples (Q, Σ. δ, q 0 , F ) where Q is a finite set of states, which is non empty. Σ is a input alphabet, indicates input set. δ is a transition function or a function defined for going to next state. q 0 is an initial state (q 0 in Q) F is a set of final states. 11. Define Non-Deterministic Finite Automation. The finite automata is called NFA when there exists many paths for a specific input from current state to next state. A finite automata is a collection of 5 tuples (Q, Σ. δ, q 0 , F ) where Q is a finite set of states, which is non empty. Σ is a input alphabet, indicates input set. δ is a transition function or a function defined for going to next state. q 0 is an initial state (q 0 in Q) F is a set of final states. S 0 S 2 q 2 S 1 1 0 1 1 0 0 S 0 S 2 q 2 S 1 1 0 1 1 0 0 q 2 q 0 q 1 q 2 0 1 0 1 1
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III Year V Semester CSE CS2303 Theory of Computation Adhiparasakthi College of Engg., G.B. Nagar, Kalavai Page 4 of 20 12. Define NFA with transition. The is a character used to indicate null string. i.e the string which is used simply for transition from one state to other state without any input. A Non Deterministic finite automata is a collection of 5 tuples (Q, Σ. δ, q 0 , F ) where Q is a finite set of states, which is non empty. Σ is a input alphabet, indicates input set. δ is a transition function or a function defined for going to next state. q 0 is an initial state (q 0 in Q) F is a set of final states. 13. Design FA wh ich accepts odd number of 1’s and any number of 0’s. 14. Design FA to check whether given unary number is divisible by three. 15. Design FA to check whether given binary number is divisible by three. S 0 S 2 q 2 S 1 1 0 1 1 0 0 S 0 S 2 q 2 S 1 0 1 1 1 0 S 3 0 0 1 q 2 q 0 q 1 q 2 0 1 1 1 1 1 q 2 q 0 q 1 q 2 q 1 1
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III Year V Semester CSE CS2303 Theory of Computation Adhiparasakthi College of Engg., G.B. Nagar, Kalavai Page 5 of 20 16. Design FA to accept the string that always ends with 00.
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