Abstract
In this paper, a family of weak constructive theories, containing arithmetic and a theory of natural-valued functions of natural arguments, is suggested. The functions are polynomially bounded and computable in time bounded by polynomials in their arguments. The languages of these theories contain functional constants for addition and multiplication and the equality predicate. Other functional constants are also allowed, provided that the corresponding functions satisfy the above conditions of polynomial boundedness. From the proofs of the theories considered witness functions for provable formulas, computable in polynomial time, can algorithmically be extracted. If an argument of a witness is a function, then the latter is used in the witness algorithm as an oracle. Bibliography: 2 titles.
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.
