be an effective enumeration of the Turing machines and let fi be the partial recursive function of a single variable that is computed by Mi. (For technical reasons it is simpler to think in terms of partial recursive functions than set (or language) recognizers.) If F1,F2,…,Fn,…
is a sequence of partial recursive functions satisfying
fi(n) is defined if and only if Fi(n) is defined,
and axiom 2:
Fi(x) ← y is a recursive predicate of i, x, and y,
then Fi(n) is a computational complexity measure and can be thought of as the amount of some “resource” consumed by Mi in computing fi(n). This notion represents a useful abstraction of the basic resources – time and space. Several remarkable theorems about computational complexity have been proved for any measure of resources satisfying the two axioms (see gap theorem, speedup theorem).
"Blums axioms." A Dictionary of Computing. . Encyclopedia.com. (August 22, 2018). http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/blums-axioms
"Blums axioms." A Dictionary of Computing. . Retrieved August 22, 2018 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/blums-axioms
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.