This course provides an introduction to the theory of computation, including formal models of computation and their relationships to formal languages. Key topics covered include automata, computability, and complexity. Students will learn about regular languages and context-free grammars, as well as limitations of computation like unsolvable problems. The goal is for students to strengthen their mathematical reasoning skills and understand the inherent capabilities and limitations of computers. Assessment includes exams, assignments, and projects. Prerequisites include discrete mathematics.

1. Theory of Computation
Course Description:
Understanding the inherent capabilities and limitations of computers is a fundamental question in
computer science. To answer this question, we will define formal mathematical models of
computation,andstudy theirrelationshipswithformal languages.Topicswill consistof three central
areas of the theory of computation: automata, computability, and complexity.
Course Objectives/StudentLearningOutcomes
StudentsLearningOutcomes. Studentswilllearnseveral formal mathematical modelsof computation
along with their relationships with formal languages. In particular, they will learn regular languages
and context free languages which are crucial to understand how compilers and programming
languages are built. Also students will learn that not all problems are solvable by computers, and
some problems do not admit efficient algorithms. Throughout this course, students will strengthen
their rigorous mathematical reasoning skills.
At the endof thiscourse,studentswillbe able todothe following:
• Studentswill demonstrateknowledge of basicmathematical modelsof computationand
describe how theyrelate toformal languages.
• Studentswill understandthatthere are limitationsonwhatcomputerscando,and learn
examples of unsolvable problems.
• Studentswill learnthatcertainproblemsdonotadmitefficientalgorithms,andidentifysuch
problems.
Program LearningOutcomes. Atthe endof the course,students:
• Will applyknowledge of computingandmathematicsappropriatetothe discipline.
• Will functioneffectivelyasamemberof a team inorderto accomplisha commongoal.
• will applymathematical foundations,algorithmicprinciplesandcomputersciencetheoryto
the modellinganddesignof computerbasedsystemsinawaythat demonstrates
• Will applydesignanddevelopmentprinciplesinthe constructionof softwaresystemsof
varyingcomplexity.
Topics
• Automata and Language: We will studysimplecomputingmodelswhichplayacrucial role in
compilersandprogramming languages.
– Finite automata,regularlanguages,andregulargrammars.
– Contextfree grammars,languages,andpushdownautomata.
– Deterministicandnondeterministicautomata.
• ComputabilityTheory: We will definemore powerful computingmodelstocapture general
computers,andlearnthat notall problemare solvable bycomputers.

2. – Turingmachines,Church’sthesis,andundecidable problems.
• ComplexityTheory:Thistheoryaimsto distinguishdecidable problemsintermsof time and
space complexity.
– Time complexityclassesPandNP.
– ReductionandNP-completeness.
– Space complexity.
A tentative week-by-weekschedule isasfollows.
• Week1. Course overview and basicconceptof Setoperations.
• Week2.Deterministicfinite automata(DFA).
• Week3. Nondeterministicfinite automata(NFA).
• Week4. Equivalence of DFA andNFA,andregularexpressions.
• Week5. Regularexpressionandregularlanguages.
• Week6. Non-regularlanguagesandpumpingLemma,andclosure properties.
• Week7. Optimal DFA and review.
• Week8. Midterm
• Week9. Context-free languages.
• Week10. Pushdownautomataandgrammarsimplification.
• Week11. Chomskynormal formandpumpinglemmaforcontext-freelanguages.
• Week12. Closure propertiesandMembershipTest
• Week13. TuringMachinesand reduction.
• Week14. NP-completeness.
• Week15. Decidabilityand recognisability.
• Week16. More complexitiesandapproximability.
• Week17. Reviewandfinal exam.
Prerequisites
• Discrete Mathematics
Textbooks
No textbookisrequired,butthe followingbookwillbe anexcellent reference.
• Introductiontothe Theoryof ComputationbyMichel Sipser,2ndEd.,Cengage Learning,
2005.

3. • IntroductiontoComputerTheory, Daniel I.A.Cohen, Prentice-Hall,SecondEdition
Allocation of Marks
Assessment Instruments Mark
Midterm examination 20%
Final Term examination 35%
Assignments/ Quizzes 10%
Reports, research projects 25%
Total 100%
Instructor
Ikram Syed,Ph.D.
• Office:GoldCampus,office:18
• Email:ikram.syed@superior.edu.pk
Simulators:
In orderto improve the pedagogyof thiscourse,interactive animationsof the variousautomata
usingavailable simulatorsare recommended.