6533b861fe1ef96bd12c59d4
RESEARCH PRODUCT
Timed Sets, Functional Complexity, and Computability
Pavel HrubešRobin CockettJoaquín Díaz-boïlsJonathan Gallaghersubject
Discrete mathematicscomplexity measurescomputabilityTheoretical computer scienceGeneral Computer ScienceBasis (linear algebra)Restriction categoriesComputabilityModuloTuring categoriesfunctional complexityTheoretical Computer ScienceDistributive propertyMathematics::Category TheoryComplexity classCategorical variableTuringcomputerPMathematicscomputer.programming_languageComputer Science(all)description
AbstractThe construction of various categories of “timed sets” is described in which the timing of maps is considered modulo a “complexity order”. The properties of these categories are developed: under appropriate conditions they form discrete, distributive restriction categories with an iteration. They provide a categorical basis for modeling functional complexity classes and allow the development of computability within these settings. Indeed, by considering “program objects” and the functions they compute, one can obtain models of computability – i.e. Turing categories – in which the total maps belong to specific complexity classes. Two examples of this are introduced in some detail which respectively have their total maps corresponding to PTIME and LOGSPACE.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-09-01 | Electronic Notes in Theoretical Computer Science |