FocusNet: Classifying better by focusing on confusing classes

Classifying Isomorphic Residue Classes

We report on a case study on combining proof planning with computer algebra systems. We construct proofs for basic algebraic properties of residue classes as well as for isomorphisms between residue classes using di erent proving techniques, which are implemented as strategies in a multi-strategy proof planner. We show how these techniques help to successfully derive proofs in our domain and ex...

Classifying Isomorphi Residue Classes

Classifying Problems into Complexity Classes

A fundamental problem in computer science is, stated informally: Given a problem, how hard is it?. We measure hardness by looking at the following question: Given a set A whats is the fastest algorithm to determine if “x ∈ A?” We measure the speed of an algorithm by how long it takes to run on inputs of length n, as a function of n. For example, sorting a list of length n can be done in roughly...

Classifying Arabic Verbs Using Sibling Classes

In the effort of building a verb lexicon classifying the most used verbs in Arabic and providing information about their syntax and semantics (Mousser, 2010), the problem of classes over-generation arises because of the overt morphology of Arabic, which codes not only agreement and inflection relations but also semantic information related to thematic arity or other semantic information like ”i...

Motivic classes of some classifying stacks

We prove that the class of the classifying stack BPGLn is the multiplicative inverse of the class of the projective linear group PGLn in the Grothendieck ring of stacks K0(Stackk) for n = 2 and n = 3 under mild conditions on the base field k. In particular, although it is known that the multiplicativity relation {T} = {S} · {PGLn} does not hold for all PGLntorsors T → S, it holds for the univer...