منابع مشابه
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 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 pro...
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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 Frege proofs. We give sentences separating quantified versions of these theories, and define a fragment ∃LA of ∀LAP in which we can interpret a weak theory V 1 of bounded arithmetic and carry out polynomial time reasoning about m...
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A colleague of ours from industry once made the following observation: \Literature professors read literature. Computer Science professors should at least occasionally read code." The point he was making was that in order to write superior prose one needs to read good (and bad) literature. Analogously, it is our thesis that exposure to elegant (and ugly) programs tends to yield the insights whi...
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General facts of linear algebra are used to give proofs for the (wellknown) existence of analogs of Kazhdan-Lusztig polynomials corresponding to formal analogs of the Kazhdan-Lusztig involution, and of explicit formulae (some new, some known) for their coefficients in terms of coefficients of other natural families of polynomials (such as the corresponding formal analogs of the Kazhdan-Lusztig ...
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ژورنال
عنوان ژورنال: Logical Methods in Computer Science
سال: 2012
ISSN: 1860-5974
DOI: 10.2168/lmcs-8(1:25)2012