Information and Computation
Restriction categories I: categories of partial maps
Theoretical Computer Science
Restriction categories III: colimits, partial limits and extensivity
Mathematical Structures in Computer Science
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
A Categorical Setting for Lower Complexity
Electronic Notes in Theoretical Computer Science (ENTCS)
Restriction categories as enriched categories
Theoretical Computer Science
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The 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.