ANNA UNIVERSITY, CHENNAI
REGULATIONS - 2013
M.E. COMPUTER SCIENCE AND ENGINEERING
CP7201 THEORETICAL FOUNDATIONS OF COMPUTER SCIENCE
To review sets, relations, functions, and other foundations
To understand propositional and predicate logics and their applications
To understand lambda calculus and functional programming
To understand graph structures and their applications
To understand formal models of computation, computability, and decidability
UNIT I FOUNDATIONS
Sets – relations – equivalence relations – partial orders – functions – recursive functions –
sequences – induction principle – structural induction – recursive algorithms – counting –
pigeonhole principle – permutations and combinations – recurrence relations
UNIT II LOGIC AND LOGIC PROGRAMMING
Propositional logic – syntax – interpretations and models – deduction theorems – normal
forms – inference rules – SAT solvers - predicate logic – syntax – proof theory – semantics
of predicate logic – undecidability of predicate logic – inferences in first-order logic – logic
programming – definite programs – SLD resolution – normal programs – SLDNF resolution –
introduction to Prolog
UNIT III LAMBDA CALCULUS AND FUNCTIONAL PROGRAMMING
Lambda notation for functions – syntax – curried functions – parametric polymorphism –
lambda reduction – alpha reduction – beta reduction – beta abstraction – extensionality
theorem – delta reduction – reduction strategies – normal forms – Church-Rosser Theorems
– pure lambda calculus – constants – arithmetic – conditionals – Iteration – recursion –
introduction to functional programming
UNIT IV GRAPH STRUCTURES
Tree Structures – Graph structures – graph representations – regular graph structures –
random graphs – Connectivity – Cycles – Graph Coloring – Cliques, Vertex Covers,
Independent sets – Spanning Trees – network flows – matching
UNIT V STATE MACHINES
Languages and Grammars – Finite State Machines – State machines and languages –
Turing Machines – Computational Complexity – computability – Decidability – Church's
Thesis
TOTAL : 45 PERIODS
OUTCOMES:
Upon Completion of the course,the students will be able
To explain sets, relations, functions
To conduct proofs using induction, pigeonhole principle, and logic
To apply counting, permutations, combinations, and recurrence relations
To apply recursive functions and lambda calculus
To explain logic programming and functional programming principles
To apply sequential structures, tree structures, and graph structures
To explain computational models, computability, and complexity
REFERENCES:
1. Uwe Schoning, “Logic for Computer Scientists”, Birkhauser, 2008.
2. M. Ben-Ari, “Mathematical logic for computer science”, Second Edition, Springer,
2003.
3. John Harrison, “Handbook of Practical Logic and Automated Reasoning”, Cambridge
University Press, 2009.
4. Greg Michaelson, “An introduction to functional programming through lambda
calculus”, Dover Publications, 2011.
5. Kenneth Slonneger and Barry Kurtz, “Formal syntax and semantics of programming
languages”, Addison Wesley, 1995.
6. Kenneth H. Rosen, “Discrete Mathematics and its applications”, Seventh Edition,
Tata McGraw Hill, 2011.
7. Sriram Pemmaraju and Steven Skiena, “Computational Discrete Mathematics”,
Cambridge University Press, 2003.
8. M. Huth and M. Ryan, “Logic in Computer Science – Modeling and Reasoning about
systems”, Second Edition, Cambridge University Press, 2004.
9. Norman L. Biggs, “Discrete Mathematics”, Second Edition, Oxford University Press,
2002.
10. Juraj Hromkovic, “Theoretical Computer Science”, Springer, 1998.
11. J. E. Hopcroft, Rajeev Motwani, and J. D. Ullman, “Introduction to Automata Theory,
Languages, and Computation”, Third Edition, Pearson, 2008.
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