|
|
| (322 intermediate revisions by more than 100 users not shown) |
| Line 1: |
Line 1: |
| {{Refimprove|date=August 2011}}
| | This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users. |
| In [[theoretical computer science]], '''Actor model theory''' concerns theoretical issues for the [[Actor model]].
| |
|
| |
|
| Actors are the primitives that form the basis of the [[Actor model]] of concurrent digital computation. In response to a message that it receives, an Actor can make local decisions, create more Actors, send more messages, and designate how to respond to the next message received. Actor model theory incorporates theories of the events and structures of Actor computations, their proof theory, and [[denotational semantics of the Actor model|denotational models]].
| | If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]] |
| | * Only registered users will be able to execute this rendering mode. |
| | * Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere. |
|
| |
|
| ==Events and their orderings==
| | Registered users will be able to choose between the following three rendering modes: |
| From the definition of an Actor, it can be seen that numerous events take place: local decisions, creating Actors, sending messages, receiving messages, and designating how to respond to the next message received.
| |
|
| |
|
| However, this article focuses on just those events that are the arrival of a message sent to an Actor.
| | '''MathML''' |
| | :<math forcemathmode="mathml">E=mc^2</math> |
|
| |
|
| This article reports on the results published in Hewitt [2006].
| | <!--'''PNG''' (currently default in production) |
| | :<math forcemathmode="png">E=mc^2</math> |
|
| |
|
| :''Law of Countability'': There are at most countably many events.
| | '''source''' |
| | :<math forcemathmode="source">E=mc^2</math> --> |
|
| |
|
| ===Activation ordering=== | | <span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples]. |
| The activation ordering (<tt>-≈→</tt>) is a fundamental ordering that models one event activating another (there must be energy flow in the message passing from an event to an event which it activates).
| |
|
| |
|
| *Because of the transmission of energy, the activation ordering is ''[[General relativity|relativistically]] [[Invariant (physics)|invariant]]''; that is, for all events <tt>e<sub>1</sub></tt>.<tt>e<sub>2</sub></tt>, if <tt>e<sub>1</sub> -≈→ e<sub>2</sub></tt>, then the time of <tt>e<sub>1</sub></tt> precedes the time of <tt>e<sub>2</sub></tt> in the relativistic [[Frame of reference|frames of reference]] of all observers.
| | ==Demos== |
|
| |
|
| *''Law of Strict Causality for the Activation Ordering'': For no event does <tt>e -≈→ e</tt>.
| | Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]: |
|
| |
|
| *''Law of Finite Predecession in the Activation Ordering'': For all events <tt>e<sub>1</sub></tt> the set <tt>{e|e -≈→ e<sub>1</sub>}</tt> is finite.
| |
|
| |
|
| ===Arrival orderings===
| | * accessibility: |
| The arrival ordering of an Actor <tt>x</tt> ( <tt>-x-> </tt>) models the (total) ordering of events in which a message arrives at <tt>x</tt>. Arrival ordering is determined by ''arbitration'' in processing messages (often making use of a digital circuit called an [[Arbiter (electronics)|arbiter]]). The arrival events of an Actor are on its [[world line]]. The arrival ordering means that the Actor model inherently has indeterminacy (see [[Indeterminacy in concurrent computation]]).
| | ** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)] |
| | ** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]]. |
| | ** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]]. |
| | ** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode. |
|
| |
|
| *Because all of the events of the arrival ordering of an actor <tt>x</tt> happen on the world line of <tt>x</tt>, the arrival ordering of an actor is ''relativistically invariant''. ''I.e.'', for all actors <tt>x</tt> and events <tt>e<sub>1</sub></tt>.<tt>e<sub>2</sub></tt>, if <tt>e<sub>1</sub> -x→ e<sub>2</sub></tt>, then the time of <tt>e<sub>1</sub></tt> precedes the time of <tt>e<sub>2</sub></tt> in the relativistic frames of reference of all observers.
| | ==Test pages == |
|
| |
|
| *''Law of Finite Predecession in Arrival Orderings'': For all events <tt>e<sub>1</sub></tt> and Actors <tt>x</tt> the set <tt>{e|e -x→ e<sub>1</sub>}</tt> is finite.
| | To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages: |
| | *[[Displaystyle]] |
| | *[[MathAxisAlignment]] |
| | *[[Styling]] |
| | *[[Linebreaking]] |
| | *[[Unique Ids]] |
| | *[[Help:Formula]] |
|
| |
|
| ===Combined ordering===
| | *[[Inputtypes|Inputtypes (private Wikis only)]] |
| The combined ordering (denoted by <tt>→</tt>) is defined to be the transitive closure of the activation ordering and the arrival orderings of all Actors.
| | *[[Url2Image|Url2Image (private Wikis only)]] |
| | | ==Bug reporting== |
| *The combined ordering is relativistically invariant because it is the transitive closure of relativistically invariant orderings. ''I.e.'', for all events <tt>e<sub>1</sub></tt>.<tt>e<sub>2</sub></tt>, if <tt>e<sub>1</sub>→e<sub>2</sub></tt>. then the time of <tt>e<sub>1</sub></tt> precedes the time of <tt>e<sub>2</sub></tt> in the relativistic frames of reference of all observers. | | If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de . |
| | |
| *''Law of Strict Causality for the Combined Ordering'': For no event does <tt>e→e</tt>.
| |
| | |
| The combined ordering is obviously transitive by definition.
| |
| | |
| In [Baker and Hewitt 197?], it was conjectured that the above laws might entail the following law:
| |
| | |
| :''Law of Finite Chains Between Events in the Combined Ordering'': There are no infinite chains (''i.e.'', linearly ordered sets) of events between two events in the combined ordering →.
| |
| | |
| ===Independence of the Law of Finite Chains Between Events in the Combined Ordering===
| |
| However, [Clinger 1981] surprisingly proved that the Law of Finite Chains Between Events in the Combined Ordering is independent of the previous laws, ''i.e.'',
| |
| | |
| Theorem. ''The Law of Finite Chains Between Events in the Combined Ordering does not follow from the previously stated laws.''
| |
| | |
| Proof. It is sufficient to show that there is an Actor computation that satisfies the previously stated laws but violates the Law of Finite Chains Between Events in the Combined Ordering.
| |
| | |
| :Consider a computation which begins when an actor ''Initial'' is sent a <tt>Start</tt> message causing it to take the following actions
| |
| :#Create a new actor ''Greeter<sub>1</sub>'' which is sent the message <tt>SayHelloTo</tt> with the address of ''Greeter<sub>1</sub>''
| |
| :#Send ''Initial'' the message <tt>Again</tt> with the address of ''Greeter<sub>1</sub>''
| |
| | |
| :Thereafter the behavior of ''Initial'' is as follows on receipt of an <tt>Again</tt> message with address ''Greeter<sub>i</sub>'' (which we will call the event <tt>'''Again<sub>i</sub>'''</tt>):
| |
| :#Create a new actor ''Greeter<sub>i+1</sub>'' which is sent the message <tt>SayHelloTo</tt> with address ''Greeter<sub>i</sub>''
| |
| :#Send ''Initial'' the message <tt>Again</tt> with the address of ''Greeter<sub>i+1</sub>''
| |
| :Obviously the computation of ''Initial'' sending itself <tt>Again</tt> messages never terminates.
| |
| | |
| :The behavior of each Actor ''Greeter<sub>i</sub>'' is as follows:
| |
| :*When it receives a message <tt>SayHelloTo</tt> with address ''Greeter<sub>i-1</sub>'' (which we will call the event <tt>'''SayHelloTo<sub>i</sub>'''</tt>), it sends a <tt>Hello</tt> message to ''Greeter<sub>i-1</sub>''
| |
| :*When it receives a <tt>Hello</tt> message (which we will call the event <tt>'''Hello<sub>i</sub>'''</tt>), it does nothing.
| |
| :Now it is possible that <tt>'''Hello<sub>i</sub>''' -''Greeter<sub>i</sub>''<tt>→ '''SayHelloTo<sub>i</sub>'''</tt> every time and therefore <tt>'''Hello<sub>i</sub>'''→'''SayHelloTo<sub>i</sub>'''</tt>.
| |
| :Also <tt>'''Again<sub>i</sub>''' -≈→ '''Again<sub>i+1</sub>'''</tt> every time and therefore <tt>'''Again<sub>i</sub>''' → '''Again<sub>i+1</sub>'''</tt>.
| |
| | |
| :Furthermore all of the laws stated before the Law of Strict Causality for the Combined Ordering are satisfied.
| |
| :However, there may be an infinite number of events in the combined ordering between <tt>'''Again<sub>1</sub>'''</tt> and <tt>'''SayHelloTo<sub>1</sub>'''</tt> as follows:
| |
| :<tt>'''Again<sub>1</sub>'''→...→'''Again<sub>i</sub>'''→...<math>\infty</math>...→'''Hello<sub>i</sub>'''→'''SayHelloTo<sub>i</sub>'''→...→'''Hello<sub>1</sub>'''→'''SayHelloTo<sub>1</sub>'''</tt>
| |
| | |
| However, we know from physics that infinite energy cannot be expended along a finite trajectory (see for example [[Quantum information and relativity theory]]). Therefore, since the Actor model is based on physics, the Law of Finite Chains Between Events in the Combined Ordering was taken as an axiom of the Actor model.
| |
| | |
| ===Law of Discreteness===
| |
| The Law of Finite Chains Between Events in the Combined Ordering is closely related to the following law:
| |
| :''Law of Discreteness'': For all events <tt>e<sub>1</sub></tt> and <tt>e<sub>2</sub></tt>, the set <tt>{e|e<sub>1</sub>→e→e<sub>2</sub>}</tt> is finite.
| |
| | |
| In fact the previous two laws have been shown to be equivalent:
| |
| | |
| :Theorem [Clinger 1981]. ''The Law of Discreteness is equivalent to the Law of Finite Chains Between Events in the Combined Ordering'' (without using the axiom of choice.)
| |
| | |
| The law of discreteness rules out [[Zeno machine]]s and is related to results on [[Petri net]]s [Best ''et al.'' 1984, 1987].
| |
| | |
| The Law of Discreteness implies the property of [[unbounded nondeterminism]]. The combined ordering is used by [Clinger 1981] in the construction of a denotational model of Actors (see [[denotational semantics]]).
| |
| | |
| ==Denotational semantics== | |
| Clinger [1981] used the Actor event model described above to construct a [[Denotational_semantics_of_the_Actor_model#Clinger.27s_Model|denotational model for Actors using power domains]]. Subsequently Hewitt [2006] augmented the diagrams with arrival times to construct a [[Denotational_semantics_of_the_Actor_model#The_Timed_Diagrams_Model|technically simpler denotational model]] that is easier to understand.
| |
| | |
| ==See also==
| |
| *[[Actor model early history]]
| |
| *[[Actor model and process calculi]]
| |
| *[[Actor model implementation]]
| |
| | |
| ==References== | |
| *Carl Hewitt, '' et al.'' '''Actor Induction and Meta-evaluation''' Conference Record of ACM Symposium on Principles of Programming Languages, January 1974.
| |
| *Irene Greif. '''Semantics of Communicating Parallel Processes''' MIT EECS Doctoral Dissertation. August 1975.
| |
| *Edsger Dijkstra. '''A discipline of programming''' Prentice Hall. 1976.
| |
| *Carl Hewitt and [[Henry Baker (computer scientist)|Henry Baker]] '''Actors and Continuous Functionals''' Proceeding of IFIP Working Conference on Formal Description of Programming Concepts. August 1-5, 1977.
| |
| *[[Henry Baker (computer scientist)|Henry Baker]] and Carl Hewitt '''The Incremental Garbage Collection of Processes''' Proceeding of the Symposium on Artificial Intelligence Programming Languages. SIGPLAN Notices 12, August 1977.
| |
| *Carl Hewitt and [[Henry Baker (computer scientist)|Henry Baker]] '''Laws for Communicating Parallel Processes''' IFIP-77, August 1977.
| |
| *Aki Yonezawa '''Specification and Verification Techniques for Parallel Programs Based on Message Passing Semantics''' MIT EECS Doctoral Dissertation. December 1977.
| |
| *Peter Bishop '''Very Large Address Space Modularly Extensible Computer Systems''' MIT EECS Doctoral Dissertation. June 1977.
| |
| *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.
| |
| *Carl Hewitt and Russ Atkinson. '''Specification and Proof Techniques for Serializers''' IEEE Journal on Software Engineering. January 1979.
| |
| *Carl Hewitt, Beppe Attardi, and Henry Lieberman. '''Delegation in Message Passing''' Proceedings of First International Conference on Distributed Systems Huntsville, AL. October 1979.
| |
| *Russ Atkinson. '''Automatic Verification of Serializers''' MIT Doctoral Dissertation. June, 1980.
| |
| *Bill Kornfeld and Carl Hewitt. '''The Scientific Community Metaphor''' IEEE Transactions on Systems, Man, and Cybernetics. January 1981.
| |
| *Gerry Barber. '''Reasoning about Change in Knowledgeable Office Systems''' MIT EECS Doctoral Dissertation. August 1981.
| |
| *Bill Kornfeld. '''Parallelism in Problem Solving''' MIT EECS Doctoral Dissertation. August 1981.
| |
| *Will Clinger. '''Foundations of Actor Semantics''' MIT Mathematics Doctoral Dissertation. June 1981.
| |
| *Eike Best. '''Concurrent Behaviour: Sequences, Processes and Axioms''' Lecture Notes in Computer Science Vol.197 1984.
| |
| *Gul Agha. '''[http://hdl.handle.net/1721.1/6952 Actors: A Model of Concurrent Computation in Distributed Systems]''' Doctoral Dissertation. 1986.
| |
| *Eike Best and R.Devillers. '''Sequential and Concurrent Behaviour in Petri Net Theory''' Theoretical Computer Science Vol.55/1. 1987.
| |
| *Gul Agha, Ian Mason, Scott Smith, and Carolyn Talcott. '''A Foundation for Actor Computation''' Journal of Functional Programming January 1993.
| |
| *Satoshi Matsuoka and [[Akinori Yonezawa]]. '''Analysis of inheritance anomaly in object-oriented concurrent programming languages''' in Research directions in concurrent object-oriented programming. 1993.
| |
| *Jayadev Misra. '''A Logic for concurrent programming: Safety''' Journal of Computer Software Engineering. 1995.
| |
| *Luca de Alfaro, Zohar Manna, Henry Sipma and Tomás Uribe. '''Visual Verification of Reactive Systems''' TACAS 1997.
| |
| *Thati, Prasanna, Carolyn Talcott, and Gul Agha. '''Techniques for Executing and Reasoning About Specification Diagrams''' International Conference on Algebraic Methodology and Software Technology (AMAST), 2004.
| |
| *Giuseppe Milicia and Vladimiro Sassone. '''The Inheritance Anomaly: Ten Years After''' Proceedings of the 2004 ACM Symposium on Applied Computing (SAC), Nicosia, Cyprus, March 14-17, 2004.
| |
| *Petrus Potgieter. [http://arxiv.org/abs/cs/0412022 '''Zeno machines and hypercomputation'''] 2005
| |
| *Carl Hewitt [http://www.pcs.usp.br/~coin-aamas06/10_commitment-43_16pages.pdf What is Commitment?Physical, Organizational, and Social] COINS@AAMAS. 2006.
| |
| | |
| [[Category:Actor model]]
| |
| [[Category:Denotational semantics]]
| |
| [[Category:Mathematics of computing]]
| |
