Theory of Computation

Introduction to The Course Lectures: Room ( Sun. & Tue.: 8 am – 9:30 am) Instructor: Dr. Ayman Srour (Ph.D. in Computer Science).

Course Description A theoretical treatment of what can be computed and how fast it can be done. Applications to compilers, string searching, and control circuit design will be discussed. The hierarchy of finite state machines, pushdown machines, context free grammars and Turing machines will be analysed, along with their variations. The notions of decidability, complexity theory and a complete discussion of NP-Complete problems round out the course.

Course Outcomes Upon successful completion of this course, the student should be able to: 1.Define languages by abstract, recursive definitions and by regular expressions. 2.Design a finite automaton to recognize a given regular language. 3.Transform a language into regular expression or finite automaton or transition graph. 4.Define deterministic and nondeterministic finite automata. 5.Prove properties of regular languages and classify them.

Course Outcomes 6.Determine decidability, finiteness and equivalence properties. 7.Define relationship between regular languages and context-free grammars. 8.Building a context-free grammar for pushdown automata. 9.Determine whether a given language is context-free language or not. 10.Prove properties of context-free languages. 11.Design Turing machine and Post machine for a given language. 12.Discuss the concept of computability.

Course Format Lectures, no lab. required. Participation in class discussion is expected. Exams: Midterm exam: 20 marks. Final exam : 60 marks. 2 assignments: 5 marks to each, total 10 marks. 2 Quizzes: 2.5 marks to each, total 5. Attendants: 5 marks.

Classroom Policies STUDENTS ARE EXPECTED TO BE ON TIME FOR LECTURES

8 Course Outline Regular Languages and their descriptors: Finite automata, nondeterministic finite automata, regular expressions. Algorithms to decide questions about regular languages, e.g., is it empty? Closure properties of regular languages.

9 Course Outline – (2) Context-free languages and their descriptors: Context-free grammars, pushdown automata. Decision and closure properties.

10 Course Outline – (3) Recursive and recursively enumerable languages. Turing machines, decidability of problems. The limit of what can be computed. Intractable problems. Problems that (appear to) require exponential time. NP-completeness and beyond.

Lecture outline Week 1: Introduction. Week 2: Basic concepts and definitions Set operations; partition of a set Equivalence relations; Properties on relation on set; Proving Equivalences about Sets. Central concepts of Automata Theory. Week 3: Regular Expressions; Operations on Regular expressions Finite Automata and Regular Expressions. Recursive definitions; Conversion from FA and regular expressions; Kleen’s Theory; Mealy Moore Machines. Conversion from Mealy to Moore and vice versa.

Lecture outline-(2) Week 4: Deterministic Finite Automata (DFA). Minimization of DFA; Non-Deterministic Finite Automata (NDFA). Week 5: Equivalence of Deterministic and Non- Deterministic Finite Automata. Week 6: Pumping Lemma for Regular Languages. Closure Properties of Regular Languages. Week 7: Context-Free Grammars; Regular Grammars; Parse Trees.

Lecture outline- (3) Week 8: Midterms Exams. Week 9: Ambiguity in Grammars and Languages. Standard Forms; Chomsky Normal Forms; Greibach normal Forms. Week 10: Pushdown Automata (PDA). Week 11: The Turing Machine. Week 12: The Halting Problem. Weeks 13 & 14: Decidability Complexity Theory.

Reference book Introduction to the Theory of Computation 2 nd Edition Michael Sipser