Abstract
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.
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Ambos-Spies, K. (2003). Problems which Cannot Be Reduced to Any Proper Subproblems. In: Rovan, B., Vojtáš, P. (eds) Mathematical Foundations of Computer Science 2003. MFCS 2003. Lecture Notes in Computer Science, vol 2747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45138-9_10
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DOI: https://doi.org/10.1007/978-3-540-45138-9_10
Publisher Name: Springer, Berlin, Heidelberg
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