Denseness of Time Hierarchy
{"Image DocumentName": "Denseness of Time Hierarchy", "Image ImageDescription": "Juris Hartmanis. Richard Stearns. Denseness of Time Hierarchy. Q: How much additional time does it. take to recognize more languages? A: At most a logarithmic factor more! Theorem: Given two time bounds t1 and t2 such that. t1(n)\u00d7log(t1(n)) = o(t2(n)),   a decidable language L. such that L\u00ceDTIME(t2(n)) but L\u00cfDTIME(t1(n)). Proof idea: Diagonalize efficiently. Note: t2(n) must be computable within t2(n) time. \u00de Time hierarchy is infinite and pretty dense!", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}