New PDF release: A Radical Approach to Algebra (Addison-Wesley Series in

By Mary Gray

ISBN-10: 020102568X

ISBN-13: 9780201025682

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Example text

4 Administrative Distance Administrative distance [3,4,5] is used for determining which entries are placed in a forwarding table when distinct protocols running on the same router have routes to common destinations. Algebraic modeling of administrative distance remains open for a careful formal treatment. One fundamental problem seems to be that capturing the way routers currently implement administrative distance leads to algebraic structures that are not distributive. In fact, we conjecture that the technique is inherently non-distributive in some sense.

E. it satisfies Equation 1. Then, providing that the algebraic structure N = (N, , ) is a semi-module, F = R M is a solution to the forwarding equation F = (A F) M. In other words, we can solve for F with F = A∗ M. Significantly, we are able to use semi-modules to model the mapping information whilst still retaining a semiring model of routing. We now develop two important semi-module constructions that model the most common manner in which routing and mapping are combined: the hot-potato and coldpotato semi-modules.

2). Assume that we are using the semiring S = (S, ⊕, ⊗) and suppose that we wish to construct forwarding matrices with elements from the idempotent, commutative semigroup N = (N, ). Furthermore, suppose that the mapping matrix M contains entries over N . In order to compute forwarding entries, it is necessary to combine routing entries with mapping entries, as before. However, we can no longer use the multiplicative operator from S because the mapping entries are of a different type. Therefore we introduce an operator ∈ (S ×N ) → N for this purpose.

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A Radical Approach to Algebra (Addison-Wesley Series in Mathematics) by Mary Gray


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