{"title":"Witness-Isomorphic Reductions and Local Search","authors":"S. Fischer, L. Hemaspaandra, L. Torenvliet","doi":"10.1201/9780429187490-7","DOIUrl":"https://doi.org/10.1201/9780429187490-7","url":null,"abstract":"We study witness-isomorphic reductions, a type of structure-preserving reduction between NP decision problems. We completely determine the relative power of the different models of witness-isomorphic reduction, and we show that witness-isomorphic reductions can be used in a uniform approach to the local search problem.","PeriodicalId":420984,"journal":{"name":"complexity, logic, and recursion theory","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129705992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
José Luis Balcázar Navarro, Ricard Gavaldà Mestre, Montserrat Hermo Huguet
{"title":"Compressibility of Infinite Binary Sequences","authors":"José Luis Balcázar Navarro, Ricard Gavaldà Mestre, Montserrat Hermo Huguet","doi":"10.1201/9780429187490-3","DOIUrl":"https://doi.org/10.1201/9780429187490-3","url":null,"abstract":"It is known that infinite binary sequences of constant \u0000Kolmogorov complexity are exactly the recursive ones. \u0000Such a kind of statement no longer holds in the presence of resource bounds. \u0000Contrary to what intuition might suggest, there are sequences of \u0000constant, polynomial-time bounded Kolmogorov complexity that are \u0000not polynomial-time computable. This motivates the study of \u0000several resource-bounded variants in search for a characterization, \u0000similar in spirit, of the polynomial-time computable sequences. \u0000We propose some definitions, based on Kobayashi's notion of \u0000compressibility, and compare them to both the standard resource-bounded \u0000Kolmogorov complexity of infinite strings, and the uniform complexity. \u0000Some nontrivial coincidences and disagreements are proved. \u0000The resource-unbounded case is also considered.","PeriodicalId":420984,"journal":{"name":"complexity, logic, and recursion theory","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121024584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}