Probabilistic Analysis of Large Finite State Machines

Regarding finite state machines as Markov chains facilitates the application of probabilistic methods to very large logic synthesis and formal verification problems. Recently, we have shown how symbolic algorithms based on Algebraic Decision Diagrams may be used to calculate the steady-state probabilities of finite state machines with more than 108 states. These algorithms treated machines with state graphs composed of a single terminal strongly connected component. In this paper we consider the most general case of systems which can be modeled as state machines with arbitrary transition structures. The proposed approach exploits structural information to decompose and simplify the state graph of the machine.

[1]  Kishor S. Trivedi.  Probability and Statistics with Reliability, Queuing, and Computer Science Applications , 1984 .

[2]  David Bryan,et al.  Combinational profiles of sequential benchmark circuits , 1989, IEEE International Symposium on Circuits and Systems,.

[3]  Terry Williams,et al.  Probability and Statistics with Reliability, Queueing and Computer Science Applications , 1983 .

[4]  Enrico Macii,et al.  Symbolic algorithms to calculate steady-state probabilities of a finite state machine , 1994, Proceedings of European Design and Test Conference EDAC-ETC-EUROASIC.

[5]  Carl Pixley,et al.  A theory and implementation of sequential hardware equivalence , 1992, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[6]  Robert K. Brayton,et al.  On Computing the Transitive Closure of a State Transition Relation , 1993, 30th ACM/IEEE Design Automation Conference.

[7]  John G. Kemeny,et al.  Finite Markov chains , 1960 .

[8]  Enrico Macii,et al.  Algebraic decision diagrams and their applications , 1993, Proceedings of 1993 International Conference on Computer Aided Design (ICCAD).