Saturation arithmetic - Revision history

98.114.141.122: /* Modern use */ copy edit, plus I added information (a correction, actually) about saturated arithmetic by software without branches

2014-10-13T06:06:16Z

Modern use: copy edit, plus I added information (a correction, actually) about saturated arithmetic by software without branches

← Older revision		Revision as of 08:06, 13 October 2014
Line 1:		Line 1:
	~~:''For the drug see [[PEPA (drug)]]''~~

	'''Performance Evaluation Process Algebra''' ('''PEPA''') is a [[stochastic]] [[process algebra]] designed for modelling computer and communication systems introduced by [[Jane Hillston]] in the 1990s.<ref>{{cite book\|last=Hillston\|first=Jane\|authorlink=Jane Hillston\|title=A Compositional Approach to Performance Modelling\|year=1996\|publisher=Cambridge University Press\|isbn=0-521-57189-8\|url=http://www.dcs.ed.ac.uk/pepa/book.pdf\|accessdate=2009-04-21}}</ref> The language extends classical process algebras such as [[Robin Milner\|Milner]]'s [[Calculus of Communicating Systems\|CCS]] and [[C.A.R. Hoare\|Hoare]]'s [[Communicating Sequential Processes\|CSP]] by introducing probabilistic branching and timing of transitions.

	~~Rates are drawn from the~~ [~~[exponential distribution]~~] and ~~PEPA models are finite-state and so give rise to a~~ [~~[stochastic process]~~], ~~specifically a [[continuous-time Markov process]] (CTMC)~~. ~~Thus~~ the ~~language can be used to study quantitative properties~~ of ~~models~~ of ~~computer and communication systems such as [[throughput]]~~, ~~[[utilisation]]~~ and ~~[[Response time (technology)\|response time]] as well as qualitative properties such as freedom from [[deadlock]].~~ ~~The language~~ is ~~formally defined using a structured [[operational semantics]]~~ in the ~~style invented by [[Gordon Plotkin]]~~.		Luke Bryan is actually [http://okkyunglee.com luke bryan tickets go on sale] a celebrity while in the creating and [http://lukebryantickets.omarfoundation.org sell tickets] also the job advancement first 2nd to his 3rd resort record, & , may be the proof. He burst open on the scene in 2013 along with his best mix of straight down-house ease of access, film star fantastic appears and words, is set t in the key way. The brand new a on the country graph or [http://www.cinemaudiosociety.org meet and greet one direction] chart and #2 around the take maps, making it the second maximum first appearance during those times of 2011 for the nation artist. <br><br>The boy of the , is aware of perseverance and dedication are important elements in terms of an effective job- . His first album, Continue to be Me, created the Top hits “All My Girlfriends Say” and “Country Man,” whilst his work, Doin’ Thing, identified the vocalist-a few right No. 3 singles: Different Getting in touch with Is really a Fantastic Point.”<br><br>Within the slip of 2003, Concerts: Luke And which had an outstanding listing of , which includes Urban. “It’s almost like you are obtaining a approval to visit to the next level, affirms these musicians that were an element of the Concertsabove right into a bigger degree of performers.” It twisted as one of the most successful excursions within its twenty-season historical past.<br><br>Stop by my website; tim mcgraw concert ([http://lukebryantickets.sgs-suparco.org go to these guys])

	~~As with most process algebras, PEPA is~~ a ~~parsimonious language. It has only four combinators, ''prefix'', ''choice'', ''co-operation'' and ''hiding''. Prefix is~~ the ~~basic building block of a sequential component~~: ~~the process (''a'', ''r'')~~.~~''P'' performs activity ''a'' at rate ''r'' before evolving to behave as component ''P''~~. ~~Choice sets up a competition between two possible alternatives: in the process (''a'', ''r'').''P'' + (''b'', ''s'').''Q'' either ''a'' wins the race (~~and ~~the process subsequently behaves as ''P'') or ''b'' wins the race (~~and the ~~process subsequently behaves as ''Q'').~~

	~~The co-operation operator requires~~ the ~~two "co-operands" to join for~~ those activities which are specified in the co-operation set: in the process ''P'' < ''a'', ''b''> ''Q'' the processes ''P'' and ''Q'' must co-operate on activities ''a'' and ''b'', but any other activities may be performed independently. The [[reversed compound agent theorem]] gives a set of ~~sufficient conditions~~ for ~~a co-operation to have a [[product form stationary distribution]].~~

	~~Finally,~~ the ~~process ''P''/{''a''} hides the activity ''a'' from view (and prevents other processes from joining with it)~~.

	~~==Syntax==~~

	~~Given a set of action names, the set of CCS processes is defined by the following [[BNF grammar]]:~~

	:<~~math~~>~~P ::= (a,\lambda).P\,\,\, \| \,\,\,P + Q\,\,\, \| \,\,\,P\stackrel{\triangleright \!\! \triangleleft}{\scriptstyle{L}}Q\,\,\, \| \,\,\,P/L\,\,\,\|\,\,\,A~~<~~/math~~>

	The ~~parts~~ of the ~~syntax~~ are, in ~~the order given above~~

	~~; action : the process <math>(a,\lambda).P</math> can perform~~ an ~~action ''a'' at rate <math>\lambda</math> and continue as the process ''P''~~.
	~~; choice :~~ the ~~process ''P+Q'' may behave as either the process ''P'' or the process ''Q''.~~
	~~; cooperation : processes ''P''~~ and ~~''Q'' exist simultaneously and behave indepdendently for actions whose names do not appear in ''L''. For actions whose names appear in ''L''~~, the ~~action must be carried out jointly and~~ a ~~race condition determines the time this takes~~.
	~~; hiding~~ : ~~the process ''P'' behaves as usual for action names not~~ in ~~''L'', and performs~~ a ~~silent action <math>\tau</math> for action names that appear in ''L''~~.
	~~; process identifier : write~~ <~~math~~>~~A \overset{\underset{\mathrm{def}}{}}{=} P~~<~~/math~~> ~~to use~~ the ~~identifier ''A''~~ to ~~refer~~ to the ~~process ''P''~~.

	~~==Tools==~~

	* [http://www.dcs.ed.ac.uk/pepa/tools/plugin/index.html PEPA Plug-~~in] for [[Eclipse (software)\|Eclipse]]<ref>{{cite doi\|10~~.~~1145/1530873.1530880}}~~<~~/ref~~>
	* [http://www.doc.ic.ac.uk/ipc/ ipc: the imperial PEPA compiler]<~~ref~~>~~{{cite doi\|10.1109/MASCOT.2003.1240679}}</ref>~~
	* [http://~~code~~.~~google~~.~~com/p/gpanalyser/ GPAnalyser] for fluid analysis of massively parallel systems<ref>{{cite doi\|10.1109/QEST.2011.26}}</ref>~~

	~~==External links==~~

	* [http://www.dcs.ed.ac.uk/pepa PEPA: Performance Evaluation Process Algebra]

	~~==References==~~

	~~{{Reflist}}~~

	~~[[Category:Process calculi]~~]

5.150.199.17 at 09:14, 4 November 2013

2013-11-04T09:14:16Z

← Older revision		Revision as of 11:14, 4 November 2013
Line 1:		Line 1:
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			'''Performance Evaluation Process Algebra''' ('''PEPA''') is a [[stochastic]] [[process algebra]] designed for modelling computer and communication systems introduced by [[Jane Hillston]] in the 1990s.<ref>{{cite book\|last=Hillston\|first=Jane\|authorlink=Jane Hillston\|title=A Compositional Approach to Performance Modelling\|year=1996\|publisher=Cambridge University Press\|isbn=0-521-57189-8\|url=http://www.dcs.ed.ac.uk/pepa/book.pdf\|accessdate=2009-04-21}}</ref> The language extends classical process algebras such as [[Robin Milner\|Milner]]'s [[Calculus of Communicating Systems\|CCS]] and [[C.A.R. Hoare\|Hoare]]'s [[Communicating Sequential Processes\|CSP]] by introducing probabilistic branching and timing of transitions.

			Rates are drawn from the [[exponential distribution]] and PEPA models are finite-state and so give rise to a [[stochastic process]], specifically a [[continuous-time Markov process]] (CTMC). Thus the language can be used to study quantitative properties of models of computer and communication systems such as [[throughput]], [[utilisation]] and [[Response time (technology)\|response time]] as well as qualitative properties such as freedom from [[deadlock]]. The language is formally defined using a structured [[operational semantics]] in the style invented by [[Gordon Plotkin]].

			As with most process algebras, PEPA is a parsimonious language. It has only four combinators, ''prefix'', ''choice'', ''co-operation'' and ''hiding''. Prefix is the basic building block of a sequential component: the process (''a'', ''r'').''P'' performs activity ''a'' at rate ''r'' before evolving to behave as component ''P''. Choice sets up a competition between two possible alternatives: in the process (''a'', ''r'').''P'' + (''b'', ''s'').''Q'' either ''a'' wins the race (and the process subsequently behaves as ''P'') or ''b'' wins the race (and the process subsequently behaves as ''Q'').

			The co-operation operator requires the two "co-operands" to join for those activities which are specified in the co-operation set: in the process ''P'' < ''a'', ''b''> ''Q'' the processes ''P'' and ''Q'' must co-operate on activities ''a'' and ''b'', but any other activities may be performed independently. The [[reversed compound agent theorem]] gives a set of sufficient conditions for a co-operation to have a [[product form stationary distribution]].

			Finally, the process ''P''/{''a''} hides the activity ''a'' from view (and prevents other processes from joining with it).

			==Syntax==

			Given a set of action names, the set of CCS processes is defined by the following [[BNF grammar]]:

			:<math>P ::= (a,\lambda).P\,\,\, \| \,\,\,P + Q\,\,\, \| \,\,\,P\stackrel{\triangleright \!\! \triangleleft}{\scriptstyle{L}}Q\,\,\, \| \,\,\,P/L\,\,\,\|\,\,\,A</math>

			The parts of the syntax are, in the order given above

			; action : the process <math>(a,\lambda).P</math> can perform an action ''a'' at rate <math>\lambda</math> and continue as the process ''P''.
			; choice : the process ''P+Q'' may behave as either the process ''P'' or the process ''Q''.
			; cooperation : processes ''P'' and ''Q'' exist simultaneously and behave indepdendently for actions whose names do not appear in ''L''. For actions whose names appear in ''L'', the action must be carried out jointly and a race condition determines the time this takes.
			; hiding : the process ''P'' behaves as usual for action names not in ''L'', and performs a silent action <math>\tau</math> for action names that appear in ''L''.
			; process identifier : write <math>A \overset{\underset{\mathrm{def}}{}}{=} P</math> to use the identifier ''A'' to refer to the process ''P''.

			==Tools==

			* [http://www.dcs.ed.ac.uk/pepa/tools/plugin/index.html PEPA Plug-in] for [[Eclipse (software)\|Eclipse]]<ref>{{cite doi\|10.1145/1530873.1530880}}</ref>
			* [http://www.doc.ic.ac.uk/ipc/ ipc: the imperial PEPA compiler]<ref>{{cite doi\|10.1109/MASCOT.2003.1240679}}</ref>
			* [http://code.google.com/p/gpanalyser/ GPAnalyser] for fluid analysis of massively parallel systems<ref>{{cite doi\|10.1109/QEST.2011.26}}</ref>

			==External links==

			* [http://www.dcs.ed.ac.uk/pepa PEPA: Performance Evaluation Process Algebra]

			==References==

			{{Reflist}}

			[[Category:Process calculi]]

41.18.191.143: Small maths typo for maximum value: corrected to 2^n-1 instead of n.

2012-04-12T15:54:09Z

Small maths typo for maximum value: corrected to 2^n-1 instead of n.

New page

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