Category theory for computing science
Category theory for computing science
Completeness in approximation classes
Information and Computation
Categories, types, and structures: an introduction to category theory for the working computer scientist
Introduction to the theory of complexity
Introduction to the theory of complexity
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Complexity and real computation
Complexity and real computation
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Identification and Recognition through Shape in Complex Systems
EUROCAST '95 Selection of Papers from the Fifth International Workshop on Computer Aided Systems Theory
EUROCAST '93 Selection of Papers from the Third International Workshop on Computer Aided Systems Theory
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Approximation problems categories
EUROCAST'05 Proceedings of the 10th international conference on Computer Aided Systems Theory
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This work presents a categorical approach to cope with some questions originally studied within Computational Complexity Theory. It proceeds a research with theoretical emphasis, aiming at characterising the structural properties of optimization problems, related to the approximative issue, by means of Category Theory. In order to achieve it, two new categories are defined: the OPT category, which objects are optimization problems and the morphisms are the reductions between them, and the APX category, that has approximation problems as objects and approximation-preserving reductions as morphisms. Following the basic idea of categorical shape theory, a comparison mechanism between these two categories is defined and a hierarchical structure of approximation to each optimization problem can be modelled.