On computing the determinant in small parallel time using a small number of processors
Information Processing Letters
A taxonomy of problems with fast parallel algorithms
Information and Control
The complexity of derivations of matrix identities
The complexity of derivations of matrix identities
Space-Efficient Counting in Graphs on Surfaces
Computational Complexity
Logical Foundations of Proof Complexity
Logical Foundations of Proof Complexity
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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 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.