We show that polynomial time Turing equivalence and a large class of other equivalence relations from computational complexity theory are universal countable Borel equivalence relations. We then discuss ultrafilters on the invariant Borel sets of these equivalence relations which are related to Martin’s ultrafilter on the Turing degrees.

Human participant performances often show evidence of learning untrained relations when conditional discrimination training between physically dissimilar stimuli is conducted. These emergent relations document equivalence class formation. The current study investigated whether class-specific consequences (i.e. the specific reinforcers used for each potential class during training) also join the...

We undertake a comprehensive study of measure equivalence between general locally compact, second countable groups, providing operator algebraic and ergodic theoretic reformulations, complete the classification amenable groups within this class up to equivalence.

Teaching arbitrary conditional discriminations and testing for derived relations may be essential for understanding changes in cognitive skills. Such conditional discrimination procedures are often used within stimulus equivalence research. For example, the participant is taught AB and BC relations and tested if emergent relations as BA, CB, AC and CA occur. The purpose of the current explorati...

Circular planar graphs are used to model electrical networks, which arise in classical physics. Associated with such a network is a network response matrix, which carries information about how the network behaves in response to certain potential differences. Circular planar graphs can be organized into equivalence classes based upon these response matrices. In each equivalence class, certain fu...

In this paper we investigate properties of a certain equivalence relation on reduced words in S, called Ca-equivalence. We combinatorially characterize the class of the lexicographically first reduced word of a permutation. We further show how this class is related to reduced words that are lattice words.

This paper is a contribution to the study of Borel equivalence relations in standard Borel spaces, i.e., Polish spaces equipped with their Borel structure. A class of such equivalence relations which has received particular attention is the class of hyperfinite Borel equivalence relations. These can be defined as the increasing unions of sequences of Borel equivalence relations all of whose equ...

We study the classification of group actions on C*-algebras up to equivariant KK-equivalence. show that any action is equivariantly KK-equivalent an a simple, purely infinite C*-algebra. conjecture Izumi equivalent equivalence between cocycle conjugacy and KK-equivalence for torsion-free amenable groups Kirchberg algebras. Let G be cyclic prime order. describe its KK-equivalence, based previous...

This paper examines the operating characteristics of a class of Tandem Banyan Switching Fabrics (TB-SFs) 1] built using Bi-Delta Networks. We use the functional equivalence between Bi-Delta Networks to induce an equivalence between TBSFs. A weaker form of equivalence guaranteeing identical performance under conditions of symmetric traac is studied, and a suucient condition for weak equivalence ...