Abstract
There is a very simple way in which the safe/normal variable discipline of Bellantoni–Cook recursion [S. Bellantoni, S. Cook, A new recursion theoretic characterization of the polytime functions, Computational Complexity 2 (1992) 97–110] can be imposed on arithmetical theories like PA: quantify over safes and induct on normals. This weakens the theory severely, so that the provably recursive functions become more realistically computable (slow growing rather than fast growing). Earlier results of D. Leivant [Intrinsic theories and computational complexity, in: D. Leivant (Ed.), Logic and Computational Complexity, Lecture Notes in Computer Science, vol. 960, Springer-Verlag, 1995, pp. 177–194] are re-worked and extended in this new context, giving proof-theoretic characterizations (according to the levels of induction used) of complexity classes between Grzegorczyk’s E 2 and E 3 .
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
