We introduce two-sorted theories in the style of [CN10] for the complexity classes L and DET, whose complete problems include determinants over Z2 and Z, respectively. We then desc...
Representation theory is a branch of algebra that allows the study of groups through linear applications, i.e. matrices. Thus problems in abstract groups can be reduced to problems...
We introduce three formal theories of increasing strength for linear algebra in order to study the complexity of the concepts needed to prove the basic theorems of the subject. We...
Abstract. We investigate the theories LA, LAP, LAP of linear algebra, which were originally defined to study the question of whether commutativity of matrix inverses has polysize F...
Lebesgue integration is a fundamental concept in many mathematical theories, such as real analysis, probability and information theory. Reported higher-order-logic formalizations o...