Settling Time Reducibility Orderings

computability theory;settling time;computation time;Pure Mathematics

Loo, Clinton

University of Waterloo

关键词: computability theory;    settling time;    computation time;    Pure Mathematics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/5101/1/Loo_Clinton.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

It is known that orderings can be formed with settling time domination and strong settling time domination as relations on c.e. sets.However, it has been shown that no such ordering can be formed when considering computation time domination as a relation on $n$-c.e. sets where $n geq 3$.This will be extended to the case of $2$-c.e. sets, showing that no ordering can be derived from computation time domination on $n$-c.e. sets when $ngeq 2$.Additionally, we will observe properties of the orderings given by settling time domination and strong settling time domination on c.e. sets, respectively denoted as $mathcal{E}_{st}$ and $mathcal{E}_{sst}$.More specifically, it is already known that any countable partial ordering can be embedded into $mathcal{E}_{st}$ and any linear ordering with no infinite ascending chains can be embedded into $mathcal{E}_{sst}$.Continuing along this line, we will show that any finite partial ordering can be embedded into $mathcal{E}_{sst}$.