On the algorithmic properties of concurrent programs

Abstract

A simple model of concurrent computations is presented in which disjoint instructions /processes/ of program are executed concurrently by processors /in a sufficiently large number/ under a shared memory environment. The semantics of such a program specifies the tree of configuration sequences which are acceptable as possible computations of the program.

We do not agree with the existing literature /e.g. [2]/ that every sharing one processor among processes can be conceived as a concurrency. We claim that the other meaning of concurrency can be defined as well. The difference between these two meanings turns out to be essential. We do not assume that each configuration is obtained from its predecessor in the computation by exactly one processor performing an atomic step /assignment or test/ in a process. On the contrary, we assume that a processor cannot be delayed during his activities. The length of a step is indefinite, it must be finite only. This reflects various speeds of processors. Hence, for the configuration in which several processors are able to start the execution of their subsequent steps, a maximal number of atomic steps will be started, the choice being nondeterministic.

We discuss semantical phenomena of concurrent computations. It is argued that they can be expressed in the language of an algorithmic logic. The problem of complete axiomatization of the latter remains open. The comparison with another model of concurrency — Petri nets — is given and, we hope, it is interesting. For, our approach offers a structured /algebraic/ restriction of the language of nets and new variants of semantics. From the results obtained in the theory of vector addition systems we learn an important property of concurrent computations — there is no faithful one processor simulation of them.