We study closure properties of measurable ultrapowers with respect to Hamkin's notion "freshness" and show that the extent these highly depends on combinatorial underlying model set theory. In one direction, a result Sakai shows that, by collapsing strongly compact cardinal become double successor cardinal, it is possible obtain theory in which such possess strongest properties. other we use va...

Analysing the properties of a probability distribution is a question of general interest. In this paper we describe the properties of the matrix-exponential class of distributions, developing some properties for the discrete case and proving the closure properties, which for the case of phase-type distributions are extended to the matrix-exponential case, this not being an immediate consequence...

Witness reduction has played a crucial role in several recent results in complexity theory. These include Toda's result that PH BP P, the \collapsing" of PH into P with a high probability; Toda and Ogiwara's results which \collapses" PH into various counting classes with a high probability; and hard functions for various function classes studied by Ogiwara and Hemachandra. Ogiwara and Hemachand...

We consider a specific class of combinatorial search or optimization problems where the search space gives rise to a closure operator and essentially the hulls are the only relevant subsets that must be checked in a brute force approach. We suggest that such a closure property can help to reduce time complexities. Moreover we propose two types of (structural) parameterization of instance classe...