Applied Computer Science II Chapter 5: Reducability

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Applied Computer Science IIChapter 5
Reducability

• Prof. Dr. Luc De Raedt
• Institut für Informatik
• Albert-Ludwigs Universität Freiburg
• Germany

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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

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Reducability
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Undecidable problems from language theory
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Computable functions

• Cf. Loop-programs
• Examples
• f(ltm,ngt)mn
• f(ltMgt) 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

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Reductions via computation histories

• Deterministic versus non-deterministic machines
• From now on we focus on deterministic machines

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Linear bound automaton

• Only limited memory available

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LBA

• LBAs are quite powerful, e.g.

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• So, LBAs are fundamentally different than TMs !

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Theorem 5.24
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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