Some finite automata models of parallel or distributed processing are studied. The first model is a collection of automata with distinct alphabets. A string over the union of the alphabets is fed to the collection, so that each automaton receives the substring consisting of characters from its alphabet. At the end of the input string, a decision to accept or reject the string is made based on the state each automaton has reached. Since the substrings may have different lengths, this model has some of the flavor of parallel processing with a final synchronization.

Many parallel computations use several synchronizations. To model this situation, the author uses several collections of automata as above, but adds a new set of synchronization states and a choice function. When, in the course of processing, each of the automata in the current collection reaches an accepting state, the process may enter a synchronization state. Then the choice function can decide to start a new collection of automata. In general, this choice may be nondeterministic: the choice function may choose any one of several possible next collections. At the end of the input string, if all of the current collections of automata are in accepting states, then the input string is accepted.

Since this approach has an element of nondeterminism, it is possible that some choices lead to acceptance while other choices lead to rejection. The author calls a model reliable if all choices lead to the same result, either acceptance or rejection. A major result of this paper is that such reliable models can be constructed.

This is a reasonable paper in finite automata theory. The theorems seem to be correct, and the misprints and undefined terms can be figured out by someone knowledgeable in the area. The difficulty that I had was in trying to figure out the relevance of the results for parallel processing. In particular, this paper deals with the acceptance of regular languages in which the symbols are supposed to represent tasks. How reasonable is it to assume that a finite number of these tasks exist? What does the accepted language represent? Can a class of sorting problems be described as such a language? Does the assumption of disjoint alphabets beg the question of how to assign tasks to processors? For the practical parallel programmer, the relevance of these results is unclear.