Theoretical Foundations of Computer Sciences ANJUMAN COLLEGE OF ENGINEERING & TECHNOLOGY Department of Computer Science & Engineering Theoretical Foundations of Computer Sciences Prof.Imteyaz Shahzad Prof. Saima Zareen Ansari

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 .

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.

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

Turing machines

┌ = Finite Set Tap Symbol Turing machine 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┌ to Q x┌ x (L,R) q0= Initial State B= Blank Symbol F= Output Mapping Function

L={anbn│n≥0}

Transition Table a b B Q0 Q1,B,R ----------------- Q4,B,S Q1 Q1,a,R Q2,B,L Q2 Q3,B,L Q3 Q3,a,L Q3,b,L Q0,B,L Q4 ----------------

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

Transition Table 1 B Q0 Q0,0,R Q0,1,R Q1,B,L Q1 Q0,1,L Q2,1,L 1 B Q0 Q0,0,R Q0,1,R Q1,B,L Q1 Q0,1,L Q2,1,L ---------------------- Q2 Q2,0,L Q3,B,S Q3 --------------------- -------------------

L={WCWr│W=(a,b)*and Wr is a reverse of W } Prof. Saima Zareen Ansari

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