Indeterminacy in concurrent computation: Difference between revisions

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'''Indeterminacy in concurrent computation''' is concerned with the effects of [[nondeterministic algorithm|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 [[multi-core processor|many-core]] computer architectures. These computer systems make use of [[arbiter (electronics)|arbiters]] which gives rise to [[nondeterministic algorithm|indeterminacy]].

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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 [[multi-core processor|many-core]] computer architectures. These computer systems make use of [[arbiter (electronics)|arbiters]] which give rise to [[nondeterministic algorithm|indeterminacy]].

==A supposed limitation of logic programming==

[[Patrick J. Hayes|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{{citation needed|date=January 2011}}.

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 [[arbiter (electronics)|arbiters]]) for determining which message is next in the [[Actor model theory#Arrival orderings|arrival ordering]] of an Actor thatwho is sent multiple messages concurrently. This introduces [[arbiter (electronics)#Arbiters give rise to indeterminacy|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]].

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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. e.g., see [[metastability in electronics]] and [[arbiter (electronics)|arbiters]]. Instead of observing the internals of arbitration processes of Actor computations, we await outcomes. Indeterminacy in arbiters produces indeterminacy in Actors. The reason that we await outcomes is that we have no alternative because of indeterminacy.

It is important to be clear about the basis for the published claim about the limitation of mathematical logic. It was not just that Actors could not, in general, be implemented in mathematical logic. The published claim was that because of the indeterminacy of the physical basis of the Actor model, that no kind of deductive mathematical logic could escape the limitation. This became important later when researchers attempted to extend [[Prolog]] (which had some basis in [[logic programming]]) to concurrent computation using message passing. (See the section below).

What does the mathematical theory of Actors have to say about this? A ''closed'' system is defined to be one which does not communicate with the outside. [[Actor model theory]] provides the means to characterize all the possible computations of a closed Actor system using the Representation Theorem [Hewitt 2007] as follows:

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==A limitation of logic due to lack of information==

An open Actor system {{mono|S}} is one in which the addresses of outside Actors can be passed into {{mono|S}} in the middle of computations so that {{mono|S}} can communicate with these outside Actors. These outside Actors can then in turn communicate with Actors internal to {{mono|S}} using addresses supplied to them by {{mono|S}}. Due to the limitation of the inability to deduce arrival orderings, knowledge of what messages are sent from outside would not enable the response of {{mono|S}} to be deduced. When other models of concurrent systems (e.g., [[process calculus|process calculi]]) are used to implement open systems, these systems also can have behavior that depends on arrival time orderings and so cannot be implemented by logical deduction.

When other models of concurrent systems (e.g., [[process calculus|process calculi]]) are used to implement open systems, these systems also can have behavior that depends on arrival time orderings and so cannot be implemented by logical deduction.

==Prolog-like concurrent systems were claimed to be based on mathematical logic==

[[Keith Clark (computer scientist)|Keith Clark]], Hervé Gallaire, Steve Gregory, Vijay Saraswat, Udi Shapiro, Kazunori Ueda, etc. developed a family of [[Prolog]]-like concurrent message passing systems using unification of shared variables and data structure streams for messages. Claims were made that these systems were based on mathematical logic.{{Citation needed|date=March 2007}} This kind of system was used as the basis of the [[fifth generation computer|Japanese Fifth Generation Project (ICOT)]].

Carl Hewitt and Gul Agha [1991] argued that these Prolog-like concurrent systems were neither deductive nor logical: like the Actor model, the Prolog-like concurrent systems were based on message passing and consequently were subject to the same indeterminacy.

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==Indeterminacy in other models of computation==

Arbitration is the basis of the indeterminacy in the [[Actor model]] of concurrent computation (see [[History of the Actor model]] and [[Actor model theory]]). It may also play a role in other models of concurrent systems, such as [[process calculus|process calculi]].

==See also==

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*Carl Hewitt. '''Viewing Control Structures as Patterns of Passing Messages''' [[Journal of Artificial Intelligence]]. June 1977.

*Henry Baker. '''Actor Systems for Real-Time Computation''' MIT EECS Doctoral Dissertation. January 1978.

*Bill Kornfeld and Carl Hewitt. '''The Scientific Community Metaphor''' [[IEEE Transactions on Systems, Man, and Cybernetics]]. January 1981.

*Will Clinger. '''Foundations of Actor Semantics''' [[MIT]] Mathematics Doctoral Dissertation. June 1981.

*Carl Hewitt. '''The Challenge of Open Systems''' Byte Magazine. April 1985. Reprinted in ''The foundation of artificial intelligence–a sourcebook'' Cambridge University Press. 1990.

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==External links==

*[http://channel9.msdn.com/Shows/Going+Deep/Hewitt-Meijer-and-Szyperski-The-Actor-Model-everything-you-wanted-to-know-but-were-afraid-to-ask Hewitt, Meijer and Szyperski: The Actor Model (everything you wanted to know, but were afraid to ask)] Microsoft Channel 9. April 9, 2012.

{{Concurrent computing}}

[[Category:Actor model (computer science)]]