What Is a State of a System? (an Outline)

We try to answer this question in deening a state as a kind of a pomset. The notion of a pomset is extended by adding to the unary predicates unary functions of bounded depth. We show the equivalence of two approaches to modeling concurrency: the sequential point of view (which is based on states) and the partial-order point of view (based on events). This note points to a possible approach for deening the semantics of communicating processes. We deene and show how to work with a natural subclass of information systems, which were introduced by Scott to give denotational domains. 1 Preface For sequential processes, a state is simply the complete information on all the variables and control positions at a particular instant. For concurrent communicating processes, the notion state has no such simple deenition, unless severe limitations on concurrency are imposed. Considering its central place, it is surprising that the general notion state has received so little attention. In this note the notion`pomset' is extended in such a way that a state is just a pomset with no temporal precedence relation on its events|it is the description of an instant (Section 3.3). This allows to demonstrate within a single framework the duality between two approaches to modeling concur-rency: the one based on events and the other on states. For one direction in this duality, any pomset is described as a serial concatenation of its states (Section 4). And for the other direction, a sequence of abstractly given states give rise to a partial order of events (Section 2). This approach to the notion of a state, and the construction of domains by Scott 1982], are used here to give a (denotational) semantics to a very simple language for concurrent processes. In fact, we modify to some extent the original deenition of information systems of Scott, and provide (in Section 6) an account of a simpliied version that suuces for our use.