Matches in SemOpenAlex for { <https://semopenalex.org/work/W3217275172> ?p ?o ?g. }
Showing items 1 to 86 of
86
with 100 items per page.
- W3217275172 endingPage "19" @default.
- W3217275172 startingPage "1" @default.
- W3217275172 abstract "We study algorithmic randomness properties for probability measures on Cantor space. We say that a measure μ on the space of infinite bit sequences is Martin-Löf absolutely continuous if the non-Martin-Löf random bit sequences form a null set with respect to μ. We think of this as a weak randomness notion for measures. We begin with examples, and provide a robustness property related to Solovay tests. The initial segment complexity of a measure μ at a length n is defined as the μ-average over the descriptive complexity of strings of length n, in the sense of either C or K. We relate this weak randomness notion for a measure to the growth of its initial segment complexity. We show that a maximal growth implies the weak randomness property, but also that both implications of the Levin-Schnorr theorem fail. We discuss C-triviality and K-triviality for measures and relate these two notions with each other. Here, triviality means that the initial segment complexity grows as slowly as possible. We show that every measure that is Martin-Löf random in the sense of Hoyrup and Rojas is Martin-Löf absolutely continuous; the converse fails because only the latter property is compatible with having atoms. In a final section we consider weak randomness relative to a general ergodic computable measure. We seek appropriate effective versions of the Shannon-McMillan-Breiman theorem and the Brudno theorem where the bit sequences are replaced by measures. We conclude with several open questions." @default.
- W3217275172 created "2021-12-06" @default.
- W3217275172 creator A5047690936 @default.
- W3217275172 creator A5085103227 @default.
- W3217275172 date "2022-01-01" @default.
- W3217275172 modified "2023-10-12" @default.
- W3217275172 title "Randomness and initial segment complexity for measures" @default.
- W3217275172 cites W1816783240 @default.
- W3217275172 cites W1997686864 @default.
- W3217275172 cites W2003864541 @default.
- W3217275172 cites W2020311636 @default.
- W3217275172 cites W2045709959 @default.
- W3217275172 cites W2049660564 @default.
- W3217275172 cites W2058444173 @default.
- W3217275172 cites W2066366917 @default.
- W3217275172 cites W2067580807 @default.
- W3217275172 cites W2070305141 @default.
- W3217275172 cites W2070615365 @default.
- W3217275172 cites W2071471193 @default.
- W3217275172 cites W2076112250 @default.
- W3217275172 cites W2101900964 @default.
- W3217275172 cites W2582697902 @default.
- W3217275172 cites W2963908355 @default.
- W3217275172 cites W2972200506 @default.
- W3217275172 doi "https://doi.org/10.1016/j.tcs.2021.11.003" @default.
- W3217275172 hasPublicationYear "2022" @default.
- W3217275172 type Work @default.
- W3217275172 sameAs 3217275172 @default.
- W3217275172 citedByCount "0" @default.
- W3217275172 crossrefType "journal-article" @default.
- W3217275172 hasAuthorship W3217275172A5047690936 @default.
- W3217275172 hasAuthorship W3217275172A5085103227 @default.
- W3217275172 hasConcept C105795698 @default.
- W3217275172 hasConcept C114614502 @default.
- W3217275172 hasConcept C118615104 @default.
- W3217275172 hasConcept C125112378 @default.
- W3217275172 hasConcept C177264268 @default.
- W3217275172 hasConcept C199360897 @default.
- W3217275172 hasConcept C202444582 @default.
- W3217275172 hasConcept C2524010 @default.
- W3217275172 hasConcept C2776809875 @default.
- W3217275172 hasConcept C2778795013 @default.
- W3217275172 hasConcept C2779341405 @default.
- W3217275172 hasConcept C2780009758 @default.
- W3217275172 hasConcept C33923547 @default.
- W3217275172 hasConcept C41008148 @default.
- W3217275172 hasConcept C55375708 @default.
- W3217275172 hasConcept C77088390 @default.
- W3217275172 hasConceptScore W3217275172C105795698 @default.
- W3217275172 hasConceptScore W3217275172C114614502 @default.
- W3217275172 hasConceptScore W3217275172C118615104 @default.
- W3217275172 hasConceptScore W3217275172C125112378 @default.
- W3217275172 hasConceptScore W3217275172C177264268 @default.
- W3217275172 hasConceptScore W3217275172C199360897 @default.
- W3217275172 hasConceptScore W3217275172C202444582 @default.
- W3217275172 hasConceptScore W3217275172C2524010 @default.
- W3217275172 hasConceptScore W3217275172C2776809875 @default.
- W3217275172 hasConceptScore W3217275172C2778795013 @default.
- W3217275172 hasConceptScore W3217275172C2779341405 @default.
- W3217275172 hasConceptScore W3217275172C2780009758 @default.
- W3217275172 hasConceptScore W3217275172C33923547 @default.
- W3217275172 hasConceptScore W3217275172C41008148 @default.
- W3217275172 hasConceptScore W3217275172C55375708 @default.
- W3217275172 hasConceptScore W3217275172C77088390 @default.
- W3217275172 hasFunder F4320320751 @default.
- W3217275172 hasFunder F4320335369 @default.
- W3217275172 hasLocation W32172751721 @default.
- W3217275172 hasOpenAccess W3217275172 @default.
- W3217275172 hasPrimaryLocation W32172751721 @default.
- W3217275172 hasRelatedWork W1516195074 @default.
- W3217275172 hasRelatedWork W1968044640 @default.
- W3217275172 hasRelatedWork W239137270 @default.
- W3217275172 hasRelatedWork W2962873506 @default.
- W3217275172 hasRelatedWork W2990180495 @default.
- W3217275172 hasRelatedWork W3014068024 @default.
- W3217275172 hasRelatedWork W3015305994 @default.
- W3217275172 hasRelatedWork W3217275172 @default.
- W3217275172 hasRelatedWork W4313349061 @default.
- W3217275172 hasRelatedWork W2144353138 @default.
- W3217275172 hasVolume "900" @default.
- W3217275172 isParatext "false" @default.
- W3217275172 isRetracted "false" @default.
- W3217275172 magId "3217275172" @default.
- W3217275172 workType "article" @default.