Symbolic algorithms to calculate steady-state probabilities of a finite state machine

Abstract

In this paper we present two symbolic algorithms to compute the steady-state probabilities for very large finite state machines. These algorithms, based on Algebraic Decision Diagrams (ADD's)/spl minus/an extension of BDDs that allows arbitrary values to be associated with the terminal nodes of the diagrams/spl minus/determine the steady-state probabilities by regarding finite state machines as homogeneous, discrete-parameter Markov chains with finite state spaces, and by solving the corresponding Chapman-Kolmogorov equations. We have implemented two solution techniques: one is based on the Gauss-Jacobi iteration, and the other one on simple matrix multiplication, we report the experimental results obtained for problems with over 10/sup 8/ unknowns in irreducible form.<>