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» Weak theories of linear algebra
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AML
2005
104views more  AML 2005»
13 years 5 months ago
Weak theories of linear algebra
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...
Neil Thapen, Michael Soltys
ITP
2010
230views Mathematics» more  ITP 2010»
13 years 7 months ago
On the Formalization of the Lebesgue Integration Theory in HOL
Lebesgue integration is a fundamental concept in many mathematical theories, such as real analysis, probability and information theory. Reported higher-order-logic formalizations o...
Tarek Mhamdi, Osman Hasan, Sofiène Tahar
DAM
2007
83views more  DAM 2007»
13 years 5 months ago
The proof theoretic strength of the Steinitz exchange theorem
We show that the logical theory QLA proves the Cayley–Hamilton theorem from the Steinitz exchange theorem together with a strengthening of the linear independence principle. Sin...
Michael Soltys
ICFP
1996
ACM
13 years 9 months ago
A Theory of Weak Bisimulation for Core CML
Concurrent ML (CML) is an extension of Standard ML of New Jersey with concurrent features similar to those of process algebra. In this paper, we build upon John Reppy's reduc...
William Ferreira, Matthew Hennessy, Alan Jeffrey
CSL
2010
Springer
13 years 6 months ago
Formal Theories for Linear Algebra
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...
Stephen Cook, Lila Fontes