A Markov Model of Certain Structured Programs

The paper is concerned with modeling the run time behavior of a certain class of programs. Each program, represented by its flowgraph, is built up from one-in/one-out constructs (after the manner of Dijkstra). The programs have neither transient states nor absorbing states. Each program has one state which possesses two cycles of relatively prime length. A program which possesses these properties is called regular. Such a program may he modeled by a finite Markov chain. It is shown that if a program is regular then its Markov model has a regular transition matrix, that is, the sequence of powers of the transition matrix converges to a matrix all of whose rows are identical. The experimental validity of the method is discussed, as are the implications of the method for program design.