Algebra for Computation

Article for analog vector algebra computation.

We introduce the concept of an analog neural network represented by chemical operations performed on strands of DNA. This new type of DNA computing has the advantage that it should be fault tolerant and thus more immune to DNA hybridization errors than a Boolean DNA computer. We describe a particular set of DNA operations to effect the interconversion of electrical and DNA data and to represent...

An algebra of reversible computation

We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules: basic reversible processes algebra, algebra of reversible communicating processes, recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.

Eecient Computation of Orthogonal Polynomials in Computer Algebra Eecient Computation of Orthogonal Polynomials in Computer Algebra

6.s897 Algebra and Computation Lecture 3

1. (Identity) There exists e ∈ G such that for all a ∈ G, a · e = a. 2. (Associativity) For all a, b, c ∈ G, a · (b · c) = (a · b) · c. Definition 2 (Group) A monoid (G, ·) is a group iff for all a ∈ G, there exists an element b ∈ G such that a · b = e. We say a group (G, ·) is commutative or Abelian iff for all a, b ∈ G, a · b = b · a. Definition 3 (Ring) For a set R and binary operators · and...

Control algebra for holonomic quantum computation with squeezed coherent states

A condition for determining the holonomy group associated to a principal bundle with connection is proven. Within the context of Holonomic Quantum Computation, this condition aids in determining the universality of the system. We apply the theory to the product bundle arising from the full two-qubit system of holonomic computation with squeezed coherent states and conclude that the control alge...