منابع مشابه
Coherence of Associativity in Categories with Multiplication
To say that C is a category with (functoral) multiplication means that there is a functor ⊗ : C → C called the multiplication where C is the category of pairs of objects and pairs of morphisms from C. [More technically, C is the category of functors and natural transformations from 2 to C where 2 is the category with objects 0 and 1, and the only morphisms are the identity morphisms.] Examples ...
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The associativity problem for the class of finite multiplication tables is known to be undecidable, even for quite narrow infinite subclasses of tables. We present criteria which can be used to decide associativity in many cases, although any effective method based on such criteria must eventually fail on a table of some size (as otherwise decidability for the general class would follow). By me...
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Several variants of hypergraph products have been introduced as generalizations of the strong and direct products of graphs. Here we show that only some of them are associative. In addition to the Cartesian product, these are the minimal rank preserving direct product, and the normal product. Counter-examples are given for the strong product as well as the non-rank-preserving and the maximal ra...
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Matrix-vector multiplication is one of the most fundamental computing primitives that has been studied extensively. Given a matrix A ∈ FN×N and a vector b ∈ FN , it is known that in the worst-caseΘ(N 2) operations over F are needed to compute Ab. Many classes of structured dense matrices have been investigated which can be represented with O(N ) parameters, and for which matrix-vector multiplic...
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We present an inference system for rst-order constrained clauses with equality modulo associativity (A). Our procedure is refutationally complete and reduces to Knuth-Bendix completion modulo A in the equational case. As an essential ingredient we present the rst |as far as we know| A-compatible reduction ordering total on the ground A-congruence classes.
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 1994
ISSN: 0893-9659
DOI: 10.1016/0893-9659(94)90017-5