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Theory of Computation Lecture 2: Mathematical Background

Summary: Theory of Computation
Lecture 2: Mathematical Background
Max Alekseyev
University of South Carolina
January 12, 2012
Lecture Outline
Strings and Languages
Lexicographic Ordering
Boolean Logic
Definitions, Theorems, and Proofs
Formal Proofs
Informal Proofs
Proof methods: construction, contradiction, induction
Strings and Languages
An alphabet is a nonempty finite set whose elements are
called symbols. E.g.: 1 = {0, 1} or
abc = {a, b, c, d, . . . , x, y, z} etc.
A string (over some fixed alphabet) is a finite sequence of
symbols. E.g.: 01001 is a sting over 1 while "samplestring"


Source: Alekseyev, Max - Department of Computer Science and Engineering, University of South Carolina


Collections: Biotechnology; Computer Technologies and Information Sciences