Cobham recursive set functions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F16%3A00456152" target="_blank" >RIV/67985840:_____/16:00456152 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.apal.2015.12.005" target="_blank" >http://dx.doi.org/10.1016/j.apal.2015.12.005</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.apal.2015.12.005" target="_blank" >10.1016/j.apal.2015.12.005</a>
Alternative languages
Result language
angličtina
Original language name
Cobham recursive set functions
Original language description
This paper introduces the Cobham Recursive Set Functions (CRSF) as a version of polynomial time computable functions on general sets, based on a limited (bounded) form of ∈-recursion. This is inspired by Cobham's classic definition of polynomial time functions based on limited recursion on notation. We introduce a new set composition function, and a new smash function for sets which allows polynomial increases in the ranks and in the cardinalities of transitive closures. We bootstrap CRSF, prove closure under (unbounded) replacement, and prove that any CRSF function is embeddable into a smash term. When restricted to natural encodings of binary strings as hereditarily finite sets, the CRSF functions define precisely the polynomial time computable functions on binary strings. Prior work of Beckmann, Buss and Friedman and of Arai introduced set functions based on safe-normal recursion in the sense of Bellantoni-Cook.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annals of Pure and Applied Logic
ISSN
0168-0072
e-ISSN
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Volume of the periodical
167
Issue of the periodical within the volume
3
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
35
Pages from-to
335-369
UT code for WoS article
000368208900008
EID of the result in the Scopus database
2-s2.0-84953293508