Stochastic Timing Machinery, Differential Equations, and Simulation

MATLAB code for interpreting arbitrary stochastic timing machine models

Abstract
Stochastic timing machinery (STM) is a diagram-oriented parallel programming language. Examples in electrical engineering, chemistry, game theory, and physics lead to associated ordinary and stochastic differential and partial differential equations. We offer an abstract mathematical definition of an algorithm for interpreting timing machine diagrams, and compact MATLAB code for implementing simulations. In particular, a Brownian particle in an arbitrary force field is modeled by a stochastic timing machine associated with the Smoluchowski Equation. For diversity, a stochastic version of the Prisoner’s Dilemma game is simulated.
We expect the mathematical theory and the technology for simulation to be accessible to a high school AP-level physics, calculus and statistics student. The STM interpreter offers opportunities for efficient parallel simulations and can compute exact solutions of associated differential equations. The technique is similar in principle to the Gillespie algorithm in computational chemistry.