arXiv subjects

Joaquín Díaz Boils

Publications and source records attributed to Joaquín Díaz Boils.

3 recordsLinked to original sources

arXiv2017

Distributive Minimization Comprehensions and the Polynomial Hierarchy

A categorical point of view about minimization in subrecursive classes is presented by extending the concept of Symmetric Monoidal Comprehension to that of Distributive Minimization Comprehension. This is achieved by endowing the former with coproducts and a finality condition for coalgebras over the endofunctor sending X to ${1}\oplus{X}$ to perform a safe minimization operator. By relying on the characterization given by Bellantoni, a tiered structure is presented from which one can obtain the levels of the Polytime Hierarchy as those classes of partial functions obtained after a certain number of minimizations.

math.CT↗

arXiv2015

A Geometry of Multimodal Systems

Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms. Subsequently, coherence results are proved pointing the connections with (usual and mixed) Distributive Laws. This is given as a geometrical description of certain axioms inside various systems with a number of necessity and possibility operators.

math.CT↗

arXiv2015

Categorical Comprehensions and Recursion

A new categorical setting is defined in order to characterize the subrecursive classes belonging to complexity hierarchies. This is achieved by means of coercion functors over a symmetric monoidal category endowed with certain recursion schemes that imitate the bounded recursion scheme. This gives a categorical counterpart of generalized safe composition and safe recursion.

math.CT↗