Algorithms_and_Data_Structures_03

Algorithms_and_Data_Structures_03 - Lecture 3 Computer...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 2
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.
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 4
Induction Axiom The induction axiom cannot be proved. There are similarities to the Peano axioms for defining natural numbers.
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern