Abstract
We show that the set of all (indices of) Turing machines running in time n2 is a complete π 01 set and that the set of all (indices of Turing machines computing characteristic functions of) recursive sets A such that PA ≠ NPA is a complete π 02 set. As corollaries we obtain results saying that some assertions concerning running time of Turing machines and some instances of the relativized P = NP problem are independent of set theory (or of another theory containing arithmetic).
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References
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© 1977 Springer-Verlag Berlin Heidelberg
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Hájek, P. (1977). Arithmetical complexity of some problems in computer science. In: Gruska, J. (eds) Mathematical Foundations of Computer Science 1977. MFCS 1977. Lecture Notes in Computer Science, vol 53. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08353-7_146
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DOI: https://doi.org/10.1007/3-540-08353-7_146
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