Problems which Cannot Be Reduced to Any Proper Subproblems
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.
KeywordsComputation Tree Turing Reducibility Cohesive Degree Oracle Machine Presentable Reducibility
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- 1.Balcazar, J.L., Diaz, J., Gabarro, J.: Structural Complexity Theory, vol. I. Springer, Berlin (1988)Google Scholar