Efficient Simulation of Forward-Branching Systems with Constructor Systems

Abstract

Strongly sequential constructor systems admit a very efficient algorithm to compute normal forms. Thatte found a transformation that allows us to simulate any orthogonal system with a constructor system. Unfortunately, this transformation does not generally preserve strong sequentiality. On the other hand, the class of forward-branching systems contains the class of strongly sequential constructor systems. Moreover, it admits a reduction algorithm similar to the reduction algorithm of the strongly sequential constructor class, but less efficient on the entire class of forward-branching systems.In this article, we present a new transformation which transforms any forward-branching system into a strongly sequential constructor system. The size of the system increases only modestly over that of the original one in many practical situations. We give an algorithm for this transformation and we prove its correctness and completeness. The new system is then proved to be equivalent to the input system, with respect to the behavior and the semantics. We then give a new transformation algorithm which increases the size of the system only linearly.

Unitary equivalence of representations of graph algebras and branching systems

“…Similarly, branching systems arise in neighboring disciplines, such as random walks, symbolic dynamics, and scientific computing (see, e.g., [10], [15], [5], [3], and [18]). …”

On graded irreducible representations of Leavitt path algebras

“…As mentioned in [16], branching systems arise in the study of various disciplines such as random walk, symbolic dynamics and scientific computing (see e.g. [15], [22], [28]). Given an arbitrary directed graph E, Gonçalves and Royer defined in [16] and [17] a branching system using a measure space (X, µ) and indicated a method of constructing a large number of representations of the graph C *algebra C * (E) in the space of bounded linear operators on L 2 (X, µ).…”

Branching Systems for Higher-Rank Graph C*-algebras

“…Branching systems arise in disciplines such as random walk, symbolic dynamics and scientific computing (see for example [9,20,29]). More recently, stimulated by Bratteli-Jorgensen's work connecting representations of the Cuntz algebra arising from iterated function systems with wavelets (see [2,3]), a large number of papers have studied representations of graph algebras from branching systems (see [6,12,13,14,15,16,17,18,19], etc).…”