Algorithms_and_Data_Structures_03

# Algorithms_and_Data_Structures_03 - Lecture 3 Computer...

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Computer Science Algorithms and Data Structures Prof. Dr. Andreas Nüchter Research I, Room 105 Jacobs University Bremen http://www.nuechti.de [email protected] Lecture 3

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Algorithms and Data Structures Dr. Andreas Nüchter September 14, 2009 70 Last Lecture Introduction of math symbols used in this lecture Specification of a computability problem: A computability problem is specified by a triple Definition of functions injective / ono-to-one surjective / onto bijective (injective and surjective) injection surjection bijcection
Algorithms and Data Structures Dr. Andreas Nüchter September 14, 2009 71 Last Lecture Definition: Power set Definition of algorithm used in this lecture An algorithm is a finite sequence of instructions that can be carried out by a real machine. The sequence of instructions causes a defined input/output behavior on the machine. A deterministic algorithm is described by a partial function from the set of possible inputs to the set of possible outputs.

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Algorithms and Data Structures Dr. Andreas Nüchter September 14, 2009 72 Last Lecture – Induction Principle Task : We want to prove that a statement holds true for a series for all Induction axiom : With other words: holds true for all iff 1. is true and 2. for all the validity of implies the validity of ,iff
Algorithms and Data Structures Dr. Andreas Nüchter September 14, 2009 73 Induction Axiom The induction axiom cannot be proved. There are similarities to the Peano axioms for defining natural numbers. Peano Axioms

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## This note was uploaded on 05/04/2010 for the course CS 320251 taught by Professor Nuechter during the Fall '09 term at Jacobs University Bremen.

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Algorithms_and_Data_Structures_03 - Lecture 3 Computer...

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