A Variant Of Chaitin's Omega function

Yuxuan Li, Shuheng Zhang, Xiaoyan Zhang +1

We investigate the continuous function $f$ defined by $$x\mapsto \sum _{\ddot{I}ƒ{\le }_{L}x}{2}^{-K(\ddot{I}ƒ)}$$ as a variant of Chaitin's Omega from the perspective of analysis, computability, and…