1. 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

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. ┌ = 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

7. L={anbn│n≥0}

8. 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

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

10. Transition Table 1 B Q0 Q0,0,R Q0,1,R Q1,B,L Q1 Q0,1,L Q2,1,L1 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

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

12. THANK YOU