We consider left-invariant control affine systems evolving on Lie groups. In this context, feedback equivalence specializes to detached feedback equivalence. We characterize (local) detached feedback equivalence in a simple algebraic manner. We then classify all (full-rank) systems evolving on three-dimensional Lie groups. A representative is identified for each equivalence class. Systems on th...

Abstract If categorical equivalence is a good criterion of theoretical equivalence, then it would seem that if some class mathematical structures represented as category, any other categorically equivalent to will have the same representational capacities. Hudetz (2019a) has presented an apparent counterexample this claim; in note, I argue fails.

Given compact non-self-intersecting planar shapes, there are a pair of ambiguities characterized by topological (in-)equivalence. When shapes are topologically inequivalent, one shape can not be continuously morphed to the other as there is no bi-continuous map (homeomorphism) between them. Thus we cannot build an isomorphism between the shapes’ standard topology. Nevertheless, one can develop ...

Checking that a given finite state program satisfies a linear temporal logic property is suffering in many cases from a severe space and time explosion. One way to cope with this is to reduce the state graph used for model checking. We define an equivalence relation between infinite sequences, based on infinite traces such that for each equivalence class, either all or none of the sequences sat...

A class of stochastic processes, denoted as marked rational arrival processes (MRAPs), is defined which is an extension of matrix exponential distributions and rational arrival processes. Continuous time Markov processes with labeled transitions are a subclass of this more general model class. New equivalence relations between processes are defined and it is shown that these equivalence relatio...

In this paper the Erdős-Rado theorem is generalized to the class of well founded trees. We define an equivalence relation on the class ds(∞)0 ( finite sequences of decreasing sequences of ordinals) with א0 equivalence classes, and for n < ω a notion of n-end-uniformity for a colouring of ds(∞)0 with μ colours. We then show that for every ordinal α, n < ω and cardinal μ there is an ordinal λ so ...

The dynamical determination of the boundary conditions in SU(N) gauge theory on the orbifold S/Z2 is investigated. We classify the equivalence classes of the boundary conditions, and then the vacuum energy density of the theory in each equivalence class is evaluated at one loop order. Unambiguous comparison of the vacuum energy densities in the two theories in different equivalence classes beco...

This paper studies the polynomial-time learnability of the classes of ordered gapped tree patterns (OGT) and ordered gapped forests (OGF) under the into-matching semantics in the query learning model of Angluin. The class OGT is a model of semi-structured database query languages, and a generalization of both the class of ordered/unordered tree pattern languages and the class of non-erasing reg...

A program schema defines a class of programs, all of which have identical statement structure, but whose expressions may differ. We define a class of syntactic similarity binary relations between linear structured schemas and show that these relations characterise schema equivalence for structured schemas which are linear, free and liberal. In this paper we prove that similarity implies equival...

All almost perfect nonlinear (APN) permutations that we know to date admit a special kind of linear self-equivalence, i.e., there exists permutation G in their CCZ-equivalence class and two A B, such °A = B °G. After providing survey on the known APN functions with focus existence self-equivalences, search for dimension 6, 7, 8 self-equivalence. In six, were able conduct an exhaustive obtain is...