Indeterminacy in concurrent computation

Indeterminacy in concurrent computation is concerned with the effects of indeterminacy in concurrent computation. Computation is an area in which indeterminacy is becoming increasingly important because of the massive increase in concurrency due to networking and the advent of many-core computer architectures. These computer systems make use of arbiters which gives rise to indeterminacy. Patrick Hayes [1973] argued that the "usual sharp distinction that is made between the processes of computation and deduction, is misleading". Robert Kowalski developed the thesis that computation could be subsumed by deduction and quoted with approval "Computation is controlled deduction." which he attributed to Hayes in his 1988 paper on the early history of Prolog. Contrary to Kowalski and Hayes, Carl Hewitt claimed that logical deduction was incapable of carrying out concurrent computation in open systems. Hewitt [1985] and Agha [1991], and other published work argued that mathematical models of concurrency did not determine particular concurrent computations as follows: The Actor model makes use of arbitration (often in the form of notional arbiters) for determining which message is next in the arrival ordering of an Actor who is sent multiple messages concurrently. This introduces indeterminacy in the arrival order. Since the arrival orderings are indeterminate, they cannot be deduced from prior information by mathematical logic alone. Therefore, mathematical logic cannot implement concurrent computation in open systems. The authors claim that although mathematical logic cannot, in their view, implement general concurrency it can implement some special cases of concurrent computation, e.g., sequential computation and some kinds of parallel computing including the lambda calculus. According to Hewitt, in concrete terms for Actor systems, typically we cannot observe the details by which the arrival order of messages for an Actor is determined. Attempting to do so affects the results and can even push the indeterminacy elsewhere.

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