Flexoelectricity: Difference between revisions

Latest revision as of 11:05, 12 December 2013

Template:Turing A Multitrack Turing machine is a specific type of Multi-tape Turing machine. In a standard n-tape Turing machine, n heads move independently along n tracks. In a n-track Turing machine, one head reads and writes on all tracks simultaneously. A tape position in a n-track Turing Machine contains n symbols from the tape alphabet. It is equivalent to the standard Turing machine and therefore accepts precisely the recursively enumerable languages.

Formal definition

A multitape Turing machine can be formally defined as a 6-tuple $M = ⟨ Q, Σ, Γ, δ, q_{0}, F ⟩$ , where

$Q$ is a finite set of states
$Σ$ is a finite set of symbols called the tape alphabet
$Γ \in Q$
$q_{0} \in Q$ is the initial state
$F \subseteq Q$ is the set of final or accepting states.
$δ \subseteq (Q ∖ A \times Σ) \times (Q \times Σ \times d)$ is a relation on states and symbols called the transition relation.
$δ (Q_{i}, [x_{1}, x_{2} . . . x_{n}]) = (Q_{j}, [y_{1}, y_{2} . . . y_{n}], d)$

where $d \in L, R$

Proof of equivalency to standard Turing machine

This will prove that a two-track Turing machine is equivalent to a standard Turing machine. This can be generalized to a n-track Turing machine. Let L be a recursively enumerable language. Let M= $⟨ Q, Σ, Γ, δ, q_{0}, F ⟩$ be standard Turing machine that accepts L. Let M' is a two-track Turing machine. To prove M=M' it must be shown that M $\subseteq$ M' and M' $\subseteq$ M

$M \subseteq M^{'}$

If all but the first track is ignored then M and M' are clearly equivalent.

$M^{'} \subseteq M$

The tape alphabet of a one-track Turing machine equivalent to a two-track Turing machine consists of an ordered pair. The input symbol a of a Turing machine M' can be identified as an ordered pair [x,y] of Turing machine M. The one-track Turing machine is:

M= $⟨ Q, Σ \times B, Γ \times Γ, δ^{'}, q_{0}, F ⟩$ with the transition function $δ (q_{i}, [x_{1}, x_{2}]) = δ^{'} (q_{i}, [x_{1}, x_{2}])$

This machine also accepts L.

References

Thomas A. Sudkamp (2006). Languages and Machines, Third edition. Adison Wesley. ISBN 0-321-32221-5. Chapter 8.6: Multitape Machines: pp 269-271

@@ Line 1: / Line 1: @@
-By investing in a premium Word - Press theme, you're investing in the future of your website. This means you can setup your mailing list and auto-responder on your wordpress site and then you can add your subscription form to any other blog, splash page, capture page or any other site you like. Your parishioners and certainly interested audience can come in to you for further information from the group and sometimes even approaching happenings and systems with the church. They found out all the possible information about bringing up your baby and save money at the same time. The number of options offered here is overwhelming, but once I took the time to begin to review the video training, I was amazed at how easy it was to create a squeeze page and a membership site. <br><br>
+{{turing}}
+A '''Multitrack [[Turing machine]]''' is a specific type of [[Multi-tape Turing machine]]. In a standard n-tape Turing machine, n heads move independently along n tracks. In a n-track Turing machine, one head reads and writes on all tracks simultaneously. A tape position in a n-track Turing Machine contains n symbols from the tape alphabet. It is equivalent to the standard Turing machine and therefore accepts precisely the recursively enumerable languages.
-Word - Press is known as the most popular blogging platform all over the web and is used by millions of blog enthusiasts worldwide. You will have to invest some money into tuning up your own blog but, if done wisely, your investment will pay off in the long run. Our Daily Deal Software plugin brings the simplicity of setting up a Word - Press blog to the daily deal space. t need to use the back button or the URL to get to your home page. As soon as you start developing your Word - Press MLM website you'll see how straightforward and simple it is to create an online presence for you and the products and services you offer. <br><br>Usually, Wordpress owners selling the ad space on monthly basis and this means a residual income source. As of now, Pin2Press is getting ready to hit the market.  If you're ready to read more in regards to [http://emailsite.de/backup_plugin_8529184 wordpress backup plugin] look into our own page. You've got invested a great cope of time developing and producing up the topic substance. Newer programs allow website owners and internet marketers to automatically and dynamically change words in their content to match the keywords entered by their web visitors in their search queries'a feat that they cannot easily achieve with older software. Premium vs Customised Word - Press Themes - Premium themes are a lot like customised themes but without the customised price and without the wait. <br><br>Word - Press installation is very easy and hassle free. php file in the Word - Press root folder and look for this line (line 73 in our example):. Websites that do rank highly, do so becaue they use keyword-heavy post titles. So, we have to add our social media sharing buttons in website. If your site does well you can get paid professional designer to create a unique Word - Press theme. <br><br>Millions of individuals and organizations are now successfully using this tool throughout the world. s ability to use different themes and skins known as Word - Press Templates or Themes. You can select color of your choice, graphics of your favorite, skins, photos, pages, etc. You should stay away from plugins that are full of flaws and bugs. 95, and they also supply studio press discount code for their clients, coming from 10% off to 25% off upon all theme deals.
+== Formal definition ==
+A multitape Turing machine can be formally defined as a 6-tuple <math>M= \langle Q, \Sigma, \Gamma,  \delta, q_0, F \rangle </math>, where
+* <math>Q</math> is a finite set of states
+* <math>\Sigma</math> is a finite set of symbols called the ''tape alphabet''
+*<math>\Gamma \in Q</math>
+* <math>q_0 \in Q</math> is the ''initial state''
+* <math>F \subseteq Q</math> is the set of ''final'' or ''accepting states''.
+*<math>\delta \subseteq \left(Q \backslash A \times \Sigma\right) \times \left( Q \times \Sigma \times d \right)</math> is a relation on states and symbols called the ''transition relation''.
+*<math>\delta \left(Q_i,[x_1,x_2...x_n]\right)=(Q_j,[y_1,y_2...y_n],d)</math>
+where <math>d \in {L,R}</math>
+== Proof of equivalency to standard Turing machine==
+This will prove that a two-track Turing machine is equivalent to a standard Turing machine. This can be generalized to a n-track Turing machine. Let L be a recursively enumerable language. Let M= <math>\langle Q, \Sigma, \Gamma,  \delta, q_0, F \rangle </math> be standard Turing machine that accepts L. Let M' is a two-track Turing machine. To prove M=M' it must be shown that M <math> \subseteq </math> M' and M' <math> \subseteq </math> M
+*<math> M  \subseteq  M' </math>
+If all but the first track is ignored then M and M' are clearly equivalent.
+*<math> M'  \subseteq  M </math>
+The tape alphabet of a one-track Turing machine equivalent to a two-track Turing machine consists of an ordered pair.  The input symbol a of a Turing machine M' can be identified as an ordered  pair  [x,y] of Turing machine M. The one-track Turing machine is:
+M= <math>\langle Q, \Sigma \times {B}, \Gamma \times \Gamma,  \delta ', q_0, F \rangle </math> with the transition function <math>\delta \left(q_i,[x_1,x_2]\right)=\delta ' \left(q_i,[x_1,x_2]\right)</math>
+This machine also accepts L.
+== References ==
+Thomas A. Sudkamp (2006). Languages and Machines, Third edition. Adison Wesley. ISBN 0-321-32221-5.  Chapter 8.6: Multitape Machines: pp 269-271
+[[Category:Turing machine]]

Flexoelectricity: Difference between revisions

Latest revision as of 11:05, 12 December 2013

Formal definition

Proof of equivalency to standard Turing machine

References

Navigation menu

Search