1 / 25

Applied Computer Science II Chapter 5: Reducability

Applied Computer Science II Chapter 5: Reducability. Prof. Dr. Luc De Raedt Institut für Informatik Albert-Ludwigs Universität Freiburg Germany. Overview. Examine several other undecidable problems Reducibility

boyce
Download Presentation

Applied Computer Science II Chapter 5: Reducability

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Applied Computer Science IIChapter 5: Reducability Prof. Dr. Luc De Raedt Institut für Informatik Albert-Ludwigs Universität Freiburg Germany

  2. Overview • Examine several other undecidable problems • Reducibility • Basic method to relate two problems to one another in the light of “(un)solvability” • Reducibility is used for various types of “unsolvability”, cf. complexity • Mapping reducibility • The Post Correspondence Problem PCP

  3. Reducability

  4. Undecidable problems from language theory

  5. Computable functions • Cf. Loop-programs • Examples : • f(<m,n>)=m+n • f(<M>) = M’ where M’ accepts the same language as TM M except that it does not move its head against the left “wall”; if M is not a TM then return epsilon

  6. Reductions via computation histories • Deterministic versus non-deterministic machines • From now on we focus on deterministic machines

  7. Linear bound automaton Only limited memory available

  8. LBA • LBAs are quite powerful, e.g.

  9. So, LBAs are fundamentally different than TMs !

  10. Theorem 5.24

  11. Conclusions • Examine several other undecidable problems • Reducibility • Basic method to relate two problems to one another in the light of “(un)solvability” • Reducibility is used for various types of “unsolvability”, cf. complexity • Mapping reducibility • The Post Correspondence Problem PCP

More Related