Independence of clones criterion - Revision history

208.22.65.78: Grammar fix.

2014-12-10T20:34:40Z

Grammar fix.

← Older revision		Revision as of 22:34, 10 December 2014
Line 1:		Line 1:
	~~{{expert-subject\|date=February 2012}}~~		Irwin Butts is what my wife enjoys to call me though I don't truly like becoming known as like that. Since she was eighteen she's been operating as a meter reader but she's usually needed her own business. To do aerobics is a thing that I'm totally addicted to. North Dakota is our beginning location.<br><br>Feel free to visit my page :: [http://www.streaming.iwarrior.net/user/WMcneil home std test]

	''~~'Probabilistic Computation Tree Logic''' (PCTL) is an extension of [[computation tree logic]] (CTL) which allows for probabilistic quantification of described properties. It has~~ been ~~defined in the paper by Hansson and Jonsson.<ref>http://citeseer.ist.psu.edu/hansson94logic.html</ref>~~

	~~PCTL is~~ a ~~useful [[logic]] for stating soft deadline properties, e~~.~~g. "after a request for a service, there~~ is ~~at least~~ a ~~98% probability~~ that ~~the service will be carried out within 2 seconds"~~. ~~Akin CTL suitability for model-checking PCTL extension~~ is ~~widely used as a property specification language for probabilistic model checkers~~.

	~~== PCTL syntax ==~~
	~~One of the possible syntax of PCTL is defined as follows:~~
	<~~center~~>
	<~~math~~>
	~~\phi~~ ::~~= p \| \neg p \| \phi \lor \phi \| \phi \land \phi \| \mathcal{P}_{\sim\lambda}(\phi \mathcal{U} \phi) \|~~
	~~\mathcal{P}_{\sim\lambda}(\square\phi)~~
	~~</math>~~
	~~</center>~~
	~~Therein, <math>\sim \in \{ <, \leq, \geq, > \}</math> is comparison operator and <math>\lambda</math> is a probability threshold.~~
	~~<br>~~
	~~Formulas of PCTL are interpreted over discrete~~ [~~[Markov chains]]. An interpretation structure~~
	~~is a quadruple <math>K = \langle S, s^i, \mathcal{T}, L \rangle</math>, where~~
	*<math>S</math> is a finite set of states,
	*<math>s^i \in S</math> is an initial state,
	*<math>\mathcal{T}</math> is a transition probability function, <math>\mathcal{T} : ~~S \times S \to [0,1] <~~/~~math>, such that for all <math>s \in S<~~/~~math> we have <math>\sum_{s'\in S} \mathcal{T}(s,s')=1</math>, and~~
	*<math>L</math> is a labeling function, <math>L:S\to2^A</math>, assigning atomic propositions to states.
	~~<br>~~
	~~A path <math>\sigma</math> from a state <math>s_0</math> is an infinite sequence of states~~
	~~<math>s_0 \to s_1 \to \dots \to s_n \to \dots </math>~~. ~~The n-th state of the path is denoted as <math>\sigma[n]</math>~~
	~~and the prefix of <math>\sigma</math> of length <math>n</math> is denoted as <math>\sigma\uparrow n</math>~~.

	~~== Probability measure ==~~
	~~A probability measure <math>\mu_m</math> of the set of path with the common prefix of length <math>n</math> is equal to the product of transitions probabilitites along the prefix of the path:~~
	~~<center><math>~~
	~~\mu_m(\{\sigma \in X : \sigma\uparrow n = s_0 \to \dots \to s_n \}) = \mathcal{T}(s_0,s_1) \times\dots\times\mathcal{T}(s_{n-1},s_n)~~
	~~</math></center>~~
	~~For <math>n = 0</math> the probability measure is equal to <math>\mu_m(\{\sigma \in X : \sigma\uparrow 0 = s_0 \}) = 1</math>~~.

	~~== Satisfaction relations ==~~
	~~Satisfaction relations <math>s \models_K f<~~/~~math>, <math>\sigma \models_K f<~~/~~math> are inductively defined as follows:~~
	* <math>s \models_K a</math> if and only if <math>a \in L(s)</math>,
	* <math>s \models_K \neg f</math> if and only if not <math>s \models_K f</math>,
	* <math>s \models_K f_1 \lor f_2</math> if and only if <math>s \models_K f_1</math> or <math>s \models_K f_2</math>,
	* <math>s \models_K f_1 \land f_2</math> if and only if <math>s \models_K f_1</math> and <math>s \models_K f_2</math>,
	* <math>s \models_K \mathcal{P}_{\sim\lambda}(f_1 \mathcal{U} f_2)</math> if and only if <math>\mu_m(\{\sigma : \sigma[0] = s \land (\exists i)\sigma[i] \models_K f_2 \land (\forall 0 \leq j < i) \sigma[j] \models_K f_1\}) \sim \lambda</math>, and
	* <math>s \models_K \mathcal{P}_{\sim\lambda}(\square f)</math> if and only if <math>\mu_m(\{\sigma : \sigma[0] = s \land (\forall i \geq 0)\sigma[i] \models_K f\}) \sim \lambda</math>.

	~~==References==~~
	~~<references />~~

	~~[[Category:Temporal logic]~~]

en>Textorus: use who for people

2013-07-20T17:25:27Z

use who for people

← Older revision		Revision as of 19:25, 20 July 2013
Line 1:		Line 1:
	~~Marvella~~ is ~~what you can contact~~ [http://~~Samedaystdtesting~~.~~com~~/~~testing-clinics~~/~~florida-fl/hialeah-std-testing/2750-west-68th-street-suite-225-226-33016 std testing~~] ~~[http://wixothek~~.~~com/user/MBuckmast~~ at ~~home std test] home her but it's not~~ the ~~most female name~~ out ~~there~~. ~~Since she was 18 she's been working~~ as a ~~receptionist but her marketing never comes~~. ~~Doing ceramics~~ is ~~what her family~~ and ~~her enjoy~~. ~~Puerto Rico~~ is where ~~he'~~s ~~always home~~ [~~http:~~//~~www.lankaclipstv.com~~/~~blog~~/~~165665 std testing at home] test kit over the [http~~://~~Rhrealitycheck~~.~~org~~/~~article~~/~~2013~~/02/22/~~trich-~~the~~-most-~~common~~-sexually-transmitted-infection-you-may-never-have-heard-~~of/ ~~counter std] test been residing but she needs~~ to ~~move simply because~~ of ~~her family members~~.<br><br>~~My weblog; [https~~://~~grouponsa.zendesk.com~~/~~entries~~/~~96807503-Items-To-Know-While-Confronting-Candida grouponsa~~.~~zendesk.com~~]		{{expert-subject\|date=February 2012}}

			'''Probabilistic Computation Tree Logic''' (PCTL) is an extension of [[computation tree logic]] (CTL) which allows for probabilistic quantification of described properties. It has been defined in the paper by Hansson and Jonsson.<ref>http://citeseer.ist.psu.edu/hansson94logic.html</ref>

			PCTL is a useful [[logic]] for stating soft deadline properties, e.g. "after a request for a service, there is at least a 98% probability that the service will be carried out within 2 seconds". Akin CTL suitability for model-checking PCTL extension is widely used as a property specification language for probabilistic model checkers.

			== PCTL syntax ==
			One of the possible syntax of PCTL is defined as follows:
			<center>
			<math>
			\phi ::= p \| \neg p \| \phi \lor \phi \| \phi \land \phi \| \mathcal{P}_{\sim\lambda}(\phi \mathcal{U} \phi) \|
			\mathcal{P}_{\sim\lambda}(\square\phi)
			</math>
			</center>
			Therein, <math>\sim \in \{ <, \leq, \geq, > \}</math> is comparison operator and <math>\lambda</math> is a probability threshold.
			<br>
			Formulas of PCTL are interpreted over discrete [[Markov chains]]. An interpretation structure
			is a quadruple <math>K = \langle S, s^i, \mathcal{T}, L \rangle</math>, where
			*<math>S</math> is a finite set of states,
			*<math>s^i \in S</math> is an initial state,
			*<math>\mathcal{T}</math> is a transition probability function, <math>\mathcal{T} : S \times S \to [0,1] </math>, such that for all <math>s \in S</math> we have <math>\sum_{s'\in S} \mathcal{T}(s,s')=1</math>, and
			*<math>L</math> is a labeling function, <math>L:S\to2^A</math>, assigning atomic propositions to states.
			<br>
			A path <math>\sigma</math> from a state <math>s_0</math> is an infinite sequence of states
			<math>s_0 \to s_1 \to \dots \to s_n \to \dots </math>. The n-th state of the path is denoted as <math>\sigma[n]</math>
			and the prefix of <math>\sigma</math> of length <math>n</math> is denoted as <math>\sigma\uparrow n</math>.

			== Probability measure ==
			A probability measure <math>\mu_m</math> of the set of path with the common prefix of length <math>n</math> is equal to the product of transitions probabilitites along the prefix of the path:
			<center><math>
			\mu_m(\{\sigma \in X : \sigma\uparrow n = s_0 \to \dots \to s_n \}) = \mathcal{T}(s_0,s_1) \times\dots\times\mathcal{T}(s_{n-1},s_n)
			</math></center>
			For <math>n = 0</math> the probability measure is equal to <math>\mu_m(\{\sigma \in X : \sigma\uparrow 0 = s_0 \}) = 1</math>.

			== Satisfaction relations ==
			Satisfaction relations <math>s \models_K f</math>, <math>\sigma \models_K f</math> are inductively defined as follows:
			* <math>s \models_K a</math> if and only if <math>a \in L(s)</math>,
			* <math>s \models_K \neg f</math> if and only if not <math>s \models_K f</math>,
			* <math>s \models_K f_1 \lor f_2</math> if and only if <math>s \models_K f_1</math> or <math>s \models_K f_2</math>,
			* <math>s \models_K f_1 \land f_2</math> if and only if <math>s \models_K f_1</math> and <math>s \models_K f_2</math>,
			* <math>s \models_K \mathcal{P}_{\sim\lambda}(f_1 \mathcal{U} f_2)</math> if and only if <math>\mu_m(\{\sigma : \sigma[0] = s \land (\exists i)\sigma[i] \models_K f_2 \land (\forall 0 \leq j < i) \sigma[j] \models_K f_1\}) \sim \lambda</math>, and
			* <math>s \models_K \mathcal{P}_{\sim\lambda}(\square f)</math> if and only if <math>\mu_m(\{\sigma : \sigma[0] = s \land (\forall i \geq 0)\sigma[i] \models_K f\}) \sim \lambda</math>.

			==References==
			<references />

			[[Category:Temporal logic]]

81.105.99.86 at 16:15, 2 September 2012

2012-09-02T16:15:36Z

New page

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