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{{turing}}
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A '''read-only Turing machine''' or '''Two-way deterministic finite-state automaton (2DFA)''' is class of models of [[computability]] that behave like a standard [[Turing machine]] and can move in both directions across input, except cannot write to its input tape. The machine in its bare form is equivalent to a [[Deterministic finite automaton]] in computational power, and therefore can only parse a [[regular language]].
 
== Theory ==
We define a standard Turing machine by the 9-tuple
 
<math>M = (Q, \Sigma, \Gamma, \vdash, \_, \delta, s, t, r)</math> where
 
* <math>Q</math> is a finite set of ''states'';
* <math>\Sigma</math> is the finite set of the ''input alphabet'';
* <math>\Gamma</math> is the finite ''tape alphabet'';
* <math>\vdash \in \Gamma - \Sigma</math> is the ''left endmarker'';
* <math>\_ \in \Gamma - \Sigma</math> is the ''blank symbol'';
* <math>\delta : Q \times \Gamma \rightarrow Q \times \Gamma \times \{L,R\}</math> is the ''transition function'';
* <math>s \in Q</math> is the ''start state'';
* <math>t \in Q</math> is the ''accept state'';
* <math>r \in Q, ~ r \ne t</math> is the ''reject state''.
 
So given initial state <math>q</math> reading symbol <math>a</math>, we have a transition defined by <math>\delta(q,a)=(q_2,a_2,d)</math> which replaces <math>a</math> with <math>a_2</math>, transitions to state <math>q_2</math>, and moves the "read head" in direction <math>d</math> (left or right) to read the next input.<ref>{{cite book |last=Kozen |first=Dexter C. |editor=David Gries, Fred B. Schneider |title=Automata and Computability |origyear=1951 |format=hardcover |edition=1 |series=Undergraduate Texts in Computer Science |year=1997 |publisher=Springer-Verlag |location=New York |isbn=0-387-94907-0 |pages=158, 210, 224}}</ref> In our 2DFA read-only machine, however, <math>a=a_2</math> always.
 
This model is now equivalent to a DFA. The proof involves building a table which lists the result of backtracking with the control in any given state; at the start of the computation, this is simply the result of trying to move past the left endmarker in that state. On each rightward move, the table can be updated using the old table values and the character that was in the previous cell. Since the original head-control had some fixed number of states, and there is a fixed number of states in the tape alphabet, the table has fixed size, and can therefore be computed by another finite state machine. This machine, however, will never need to backtrack, and hence is a DFA.
 
=== Variants ===
 
Several variants of this model are also equivalent to DFAs. In particular, the nondeterministic case (in which the transition from one state can be to multiple states given the same input) is reducible to a DFA.
 
Other variants of this model allow more [[computational complexity]]. With a single infinite [[stack (data structure)|stack]] the model can parse (at least) any language that is computable by a Turing machine in [[linear time]].<ref>''Computational Complexity'' by Wagner and Wechsung, section 13.3 (1986, ISBN 90-277-2146-7)</ref> In particular, the language {a<sup>n</sup>b<sup>n</sup>c<sup>n</sup>} can be parsed by an algorithm which verifies first that there are the same number of a's and b's, then rewinds and verifies that there are the same number of b's and c's. With the further aid of [[Nondeterministic finite automaton|nondeterminism]] the machine can parse any [[context-free language]]. With two infinite stacks the machine is [[Turing equivalent]] and can parse any recursive [[formal language]].
 
If the machine is allowed to have multiple tape heads, it can parse any language in [[L (complexity)|L]] or [[NL (complexity)|NL]], according to whether nondeterminism is allowed.<ref>''Computational Complexity'' by Wagner and Wechsung, section 13.1 (1986, ISBN 90-277-2146-7)</ref>
 
== Applications ==
 
A read-only Turing machine is used in the definition of a [[Universal Turing machine]] to accept the definition of the Turing machine that is to be modelled, after which computation continues with a standard Turing machine.
 
In modern research, the model has become important in describing a new complexity class of [[Quantum finite automata]] or deterministic [[Probabilistic automaton|probabilistic automata]].<ref>{{cite journal |last=Kondacs |first=A. |authorlink= |coauthors=J. Watrous |year=1997 |month= |title=On the power of quantum finite state automata |journal=38th Annual Symposium on Foundations of Computer Science (FOCS '97) |volume= |issue= |pages=66–75 |id= |url=http://www.cs.uwaterloo.ca/~watrous/papers/qfa.ps |accessdate= 2007-11-07 |quote=|doi=10.1109/SFCS.1997.646094|format= &ndash; <sup>[http://scholar.google.co.uk/scholar?hl=en&lr=&q=author%3A+intitle%3AOn+the+power+of+quantum+finite+state+automata&as_publication=38th+Annual+Symposium+on+Foundations+of+Computer+Science+%28FOCS+%2797%29&as_ylo=1997&as_yhi=1997&btnG=Search Scholar search]</sup> |archiveurl = http://web.archive.org/web/20070823235100/http://www.cs.uwaterloo.ca/~watrous/papers/qfa.ps <!-- Bot retrieved archive --> |archivedate = 2007-08-23}} {{dead link|date=June 2008}}</ref><ref>{{cite journal |last1=Dwork |first1=Cynthia |authorlink1=Cynthia Dwork |last2=Stockmeyer |first2=Larry |authorlink2=Larry Stockmeyer |year=1990 |month= |title=A Time Complexity Gap For 2-Way Probabilistic Finite State Automata |journal=SIAM Journal on Computing |volume=19 |issue=6 |pages=1011–1023 |id= |url=http://www.geocities.com/stockmeyer@sbcglobal.net/pfa_gap.ps |accessdate= 2007-11-07 |quote=|doi=10.1137/0219069 |archiveurl=http://www.webcitation.org/query?url=http://www.geocities.com/stockmeyer%40sbcglobal.net/pfa_gap.ps&date=2009-10-25+22:24:09|archivedate=2009-10-26}}</ref>
 
== See also ==
* [[Computability]]
* [[Turing machine equivalents]]
* [[Stack machine]]
* [[Queue automaton]]
* [[Quantum computer]]
 
== References ==
 
{{reflist}}
 
==External links==
* [http://www.webber-labs.com/fl/lectures/ppt-slides/09.ppt Lecture on finite-state automata by Adam Webber]
 
{{DEFAULTSORT:Read-Only Turing Machine}}
[[Category:Turing machine]]

Latest revision as of 16:33, 17 November 2014

Zits affects over ninety% of teenagers and can also be very common in younger adults and pregnant women. Sadly, we have now to take care of embarrassing pimples in some situation. Since there are few research associated to the pregnancy and Tretinoin cream it is not advisable to use it on pregnant girls. You'll have already seen various Tretinoin cream commercials all over the internet by Canadian 't purchase medicines from those pretend on-line pharmacies. Obagi is the primary brand for Obagi cream and they've been the trade for more than years you have to be thinking methods to purchase them. Tretinoin cream ought to be utilized once daily before bed time. This can be a good remedy.

So, if you want to have a younger-trying healthy skin, include software of vitamin E pores and skin cream in your daily beauty regimen! Caution: Previous to making use of this pores and skin cream, it is advised to do a patch check as it may cause irritation in people who have extraordinarily sensitive pores and skin. Another factor to keep in mind is that the results of this cream take a while to indicate on the skin. Remedy with this cream eliminates the roughness of the pores and skin.

To eliminate pimples, a single cream or a single face wash is usually not enough, you should maintain the skin through appropriate products plus medication if needed. Need to be non-comedogenic, that's, products that do not cause zits. I've a really oily pores and skin & get pimples at regular intervals. I used Cleargel for acne and dark spot as per dermatologist. Hi rajkamal, welcome to Zits Mantra.

The whitening creams prescribed by the physician assist to mix dark zits scars into your pores and skin with out leaving any hint. For severe acne scars, the doctor would possibly advocate few sessions of chemical substances peels, and then ask one to continue using the cream, after few days of peel functions. When a prescription whitening cream is combined with chemical peels therapy, it may assist to lighten or cut back the looks of this pores and skin problem faster. It should be used sparingly as an excessive amount of can hurt your pores and skin.

Once 60% of the inflammatory zits received removed consumption of antibiotics ought to stopped. The status of the producer can also play an important role when choosing an pimples scar remover Look out for the variety of years they have been in business and any legal battles they might have had with their products. For whiteheads, exfoliating pimples lotions similar to glycolic acid primarily based ones work higher.

The perfect solution is to make use of a cream that may dry out your pimples and pimples. Severe pimples is a medical condition so that you shouldn't be ashamed to seek the advice of your doctor about it. The identical goes you probably have acne on your again or other parts of the upper body. If easy over-the-counter options don't work for you and you suffer from severe zits, it's possible you'll need to attempt a prescription cream. To prescribe this, your physician should assess the reason for your acne and the way severe it's. I've a Oily pores and skin.



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