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Review of Mathematical Terms and Theory Basic mathematical notations and set theory, Logic functions and relations, Language definitions, Mathematical inductions and recursive definitions. Finite Automata Deterministic and non deterministic finite automata, -Transitions, Conversion from NFA to DFA, Kleene's theorem, Regular and non regular languages. CFG (Context Free Grammar) Introduction to CFG, CFG and known languages, Unions concatenations and *'S notations and CFL, Derivations of trees and ambiguity, Unambiguous CFG and algebric expressions, Normal forms and siplified forms. Pushdown Automata, CFL and NFL Introduction to PDA, Definition, DPDA, PDA corresponding to CFG, CFG corresponding to PDA, Introduction to CFL, Intersections and complements of CFL, Decisions problems and CFL Turing Machines, Recursive Language Model of computation and church turning thesis, Definition of turing machine, Tm and language acceptors, Variations of Tm, Non deterministic Tm, Universal Tm, Enumerable and language, Recursive and non recursive enumerable. Computation Functions, Measuring, Classifications and Complexity Primitive recursive functions, Halting problem, Recursive predicates and some bounded operations, Unbounded minimizations and m - Recursive functions, Godel numbering, Computable functions and m - Recursive, Numerical functions. Tractable and Intractable Problems Growth rate and functions, Time and speed complexity, Complexity classes, Tractable and possibly intractable problems, P and Np completeness, Reduction of time, Cook's theorem, Np-complete problems.