Cook, Stephen A and Fontes, Lila A - Formal Theories for Linear Algebra

lmcs:716 - Logical Methods in Computer Science, March 16, 2012, Volume 8, Issue 1
Formal Theories for Linear Algebra

Authors: Cook, Stephen A and Fontes, Lila A

We introduce two-sorted theories in the style of [CN10] for the complexity classes \oplusL and DET, whose complete problems include determinants over Z2 and Z, respectively. We then describe interpretations of Soltys' linear algebra theory LAp over arbitrary integral domains, into each of our new theories. The result shows equivalences of standard theorems of linear algebra over Z2 and Z can be proved in the corresponding theory, but leaves open the interesting question of whether the theorems themselves can be proved.

DOI : 10.2168/LMCS-8(1:25)2012
Volume: Volume 8, Issue 1
Published on: March 16, 2012
Submitted on: January 10, 2011
Keywords: Computer Science - Logic in Computer Science,F.4.0


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