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ANJUMAN COLLEGE OF ENGINEERING & TECHNOLOGY Department of Computer Science & Engineering

ANJUMAN COLLEGE OF ENGINEERING & TECHNOLOGY Department of Computer Science & Engineering Theoretical Foundations of Computer Sciences Prof.Imteyaz Shahzad. Syllabus:.

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ANJUMAN COLLEGE OF ENGINEERING & TECHNOLOGY Department of Computer Science & Engineering

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  1. ANJUMAN COLLEGE OF ENGINEERING & TECHNOLOGY Department of Computer Science & Engineering Theoretical Foundations of Computer Sciences Prof.ImteyazShahzad

  2. Syllabus: • Unit 1: Mathematical preliminaries –Sets, operations, relations, strings, closure of relation, countability and diagonalization, induction and proof methods- pigeon-hole principle ,concept of language, formal grammars, Chomsky hierarchy. • Unit 2: Finite Automaton, regular languages, deterministic & non deterministic finite automata, ϵ-closures, minimization of automata, equivalence, Moore and Mealy machine. • Unit 3: Regular expression, identities, Regular grammar, right linear, left linear, Arden theorem, Pumping lemma for regular sets, closure & decision properties for regular sets, Context free languages, parse trees and ambiguity, reduction of CFGS, Normal forms for CFG .

  3. Unit 4:Push down Automata (PDA), non-determinism, acceptance by two methods and their equivalence, conversion of PDA to CFG, CFG to PDAs, closure and decision properties of CFLs, pumping lemma for CFL. • Unit 5:Turing machines, TM as acceptor, TM as transducers, Variations of TM, linear bounded automata, TM as computer of function. • Unit 6:Recursively enumerable (r.e.) set, recursive sets, Decidability and solvability, Post correspondence Problem (PCP), Introduction to recursive function theory, primitive recursive functions, Ackerman function.

  4. COURSE OUTCOMES: • CO1: Classify the concept of languages and automata. • CO2: Explain the formal relationships among machines, languages and grammars. • CO3: Construct Regular Grammar and normal forms for CFG. • CO4: Design and develop finite automata for given regular language. • CO5: Design Push Down Automata, Turing Machine for given languages • CO6: Demonstrate use of computability, decidability, recursive function theory through problem solving

  5. Turing machines

  6. Turingmachine consist of 7 TUPLE: M=(Q, Ʃ,┌ , δ, qo, B, F) Q= Set of Finite State Ʃ= Set of Alphabet ┌ = Finite Set Tap Symbol δ = Transition Function Mapping From Q x┌ toQ x┌ x (L,R) q0= Initial State B= Blank Symbol F= Output Mapping Function

  7. L={anbn│n≥0}

  8. Transition Table

  9. Design a Turing Machine For 2’s Compliment of binary number.

  10. Transition Table

  11. L={WCWr│W=(a,b)*and Wris a reverse of W }

  12. THANK YOU

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