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'''Configuration graphs''' are a theoretical tool used in [[computational complexity theory]] to prove a relation between [[Graph (mathematics)|graph]] [[reachability]] and [[Computational_complexity_theory#Complexity_classes|complexity classes]].
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== Definition ==
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A theoretical computational model, like [[Turing machine]] or [[finite automata]], explains how to do a computation. The model explains both what is an initial configuration of the machine and which steps can be taken to continue the computation, until we eventually stop. A ''configuration'', also called an ''Instantaneous Description(ID)'' is a finite representation of the machine at a given time. For example, for a finite automata and a given input, the configuration will be the current state and the number of read letters, for a Turing machine it will be the state, the content of the tape and the position of the head. A configuration graph is a directed [[labeled graph]] where the label of the vertices are the possible configurations of the models and where there is an edge from one configuration to another if it correspond to a computational step of the model.
 
The initial and accepting configuration(s) of the machine are special vertices of the configuration graph. The computation accepts if and only if there is a path from an initial vertex to an accepting vertex.
 
==Useful property==
If the computation is deterministic then from any configuration there is at most one possible step, so the graph is of out-degree 1, and there is exactly one initial state.
 
Once we add a dummy initial vertex with an edge to every initial vertex and a dummy accepting vertex with an edge from every accepting vertex, checking if there is an accepting computation only requires to check if there is a path from the initial vertex to the accepting vertex, which is the [[reachability]] problem.
 
A cycle in the graph means that there is a possible infinite loop in the computation.
 
==Size of the graph==
The computational graph can be of infinite size if there are no restrictions on possible configurations; indeed, it is easy to see that there are Turing machines which can reach arbitrarily large configurations.
 
It is also possible to have finite graphs: on [[Deterministic finite automaton]] with <math>s</math> sates, for a given word of size <math>n</math> the configuration is composed of the position of the head and the current state. So the graph is of size <math>(n+1)s</math>, and the accessible part from the intitial state is of size <math>n+1</math>.
 
== Use of this object ==
This notion is useful because it reduces computational problems to graph [[reachability]] problems.
 
For example, since [[reachability]] is in [[NL (complexity)|NL]] when we can represent configurations in space which is logarithmic in the size of the input, and since the configuration of the Turing Machine in [[NL (complexity class)|NL]] is indeed of logarithmic size, then graph-reachability is [[Complete (complexity)|complete]] for NL.<ref name="papa">[[Christos Papadimitriou|Papadimitriou, Christos H.]]&#32;(1994). ''Computational Complexity'', Reading, Massachusetts:&#32;Addison-Wesley. ISBN 0-201-53082-1.</ref>
 
In the other direction, it helps to verify the complexity of a computation model; the decision problem for a (deterministic) model whose configuration are of space which is logarithmic in the size of the input is in ([[L (complexity)|L]]) [[NL (complexity)|NL]]. This is for example the case of finite automata and finite automata with one counter.
 
== References ==
{{Reflist}}
* {{cite book|author = [[Sanjeev Arora]] and [[Boaz Barak]] | year = 2009 | title = Computational complexity, a modern approach | publisher= Cambridge University Press | isbn = 978-0-521-42426-4}} Section 4.3: NL-completeness, p.&nbsp;87.
 
{{DEFAULTSORT:Computational Complexity Theory}}
[[Category:Computational complexity theory|*]]

Latest revision as of 10:30, 24 October 2014

While this mindset is certainly understandable, it simply isn't practical at that price point. A little more than 30 miles, with a 5,200 foot elevation gain, and you'll ride over the finish line. The suspension choice of these frames is called pneumatic shocks. If the skin diameter is smaller than a quarter do not be surprised if you must change them a couple of instances per season to keep the bike working reliably. If you have any queries pertaining to wherever and how to use Info size bike mountain bike sizing., you can get hold of us at our own page. Two hunters may choose to use trailers if their distance from the truck is over four or five miles.

Adjust the tyre pressure too so it is at its optimum level. If you're planning on doing mostly road biking with the occasional cross country trip, and only once in a while going down an actual mountain. So how exactly would you go about making this dream a reality. You can travel on the equivalent of 10 cents a gallon of gas. Now the most successful business gurus are looking to the interns for lessons.

They have great suspension that fits the need of both amateur and professional bikers. You always have to be ready while riding your bike. The tube sits next to your mouth so you can sip as you ride. It is pretty incredible how much of a significant difference Haro mountain bike can have, of course you have to think about certain factors. We have built a number of thousand semi custom wheels for all kinds of bikes, and will probably be happy to do the exact same for you.

Most people will increase the power and size of their electric motor with the purpose of traveling at a higher speed and increasing the torque of the bike. Bikes are a great way to get around - they're fun, they're cheap to fuel (they burn only calories) and they're a great way to get fit. Mountain biking is all about stretching your limits, enjoying the ambience, feel the mood swings of mountains weather and then reaching to the final destination. Putting is difficult, when you are just starting out getting on the green is great, but as you get better you want to put your ball as close to the pin as you can. Scott Motorcycles has been plauged with a popularity of availableness problems on their higher end motorbikes and it looks like 2012 will not be any different.

In the recent article section, you can find the list of biking related articles with a detailed description present on the official website. There is anything from shocks to gears, special wheels, exclusive take care of bars that can be immediately switched to match the terrain you're riding on and so substantially much more. One of the main concerns for any cyclist is safety, having the right kit is a must. Sign up to get a mountain bike expedition and relive people childhood biking wonder and thrills with a whole new tier. Part of Park City's distinction as the International Mountain Bike Association's first and only gold-level Ride Center is its abundance of beginner trails.

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