Problems which Cannot Be Reduced to Any Proper Subproblems

  • Klaus Ambos-Spies
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)


For any reducibility ≤ r , an infinite set A is called introimmune under r-reducibility if any subset B of A to which A can be r-reduced is a finite variant of A. We show that there is a recursive – in fact exponential-time computable – set which is introimmune under polynomial-time bounded Turing reducibility. More generally, there are recursive introimmune sets for all recursively presentable reducibilities. This answers some questions of Cintioli and Silvestri.


Computation Tree Turing Reducibility Cohesive Degree Oracle Machine Presentable Reducibility 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Klaus Ambos-Spies
    • 1
  1. 1.Department of Mathematics and Computer ScienceRuprecht-Karls-Universität HeidelbergHeidelbergGermany

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