Program schemas with concurrency: execution time and hangups

A class of program schemas with concurrency is defined as a natural extension of the standard notion of sequential flow-chart-like schemas. The question is considered as to whether such a program schema may reach a premature termination (or "hangup") for some interpretation. It is shown that in general this question is undecidable; however, it is shown to be decidable for the class of free program schemas. And an algorithm for testing this property is presented with an upper time bound that grows linearly with the size of the schema.Several structural properties are shown to be equivalent to the hangup-free conditon for free schemas. And we give a method for computing the expected execution time of a program schema if the expected frequencies of choices at the branch points are known.