Theory of Computation: alphabet and languages

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What is this subject called Theory of Computation? 
It is one of most important topic of computer science. It involves heavy use of mathematics. 
What is taught in the subject ?
 
computer uses algorithms than receive input and produce precise output. The algorithm themselves are nothing but mathematical functions. These functions receives inputs and gives outputs consistently.
 
but certain class of mathematical functions does not have any algorithms, or algorithms that does not work on all inputs.
 
There is graph associated with every function and this graph of f consists of a pair 
graph(f(x))=(x,f(x) ). 
If a function has this set or tuple, then that function admit algorithms that solve problems for given input.
 
Theory of Computation is to find whether a given input belongs to this set, this problem is known as the set membership problem.
 
We try to solve this set membership problems for given strings or languages.
 

Fundamental concepts

Symbols

Any single object is called symbol.

for example:-

1,0, A , a , @ , # are symbols.

Alphabets

Alphabet is finite, non-empty set of symbols denoted by Σ.

Σ = { 0,1 } , Σ = {a,b,c} are examples of alphabet.


Strings or words over Σ

Consider alphabet , Σ = { 0,1 }

w3= 010 ,  w4= 0111

Suppose the alphabet is Σ = { a, ε}

w = a ε = ε a = a , where ε is an empty string.


length of string

It is the number of symbols in the string w. The length of empty string is 0.

|ε | = 0

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| w| = | a a b a| = 4 ,

It does not matter if the alphabets are repeated.

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Concatenation of strings

It is nothing but to join two shorter strings to make a single larger string. 
w3= 010 ,  w4= 0111


w7 = 0100111 is concatenation of w3 .  w4  .

w1 w2 = ε . b = b . ε = b , where w1 = ε and w2 = b

 

 

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  184. Hey I know this is off topic but I was wondering if you knew of any widgets I could add to my blog that automatically tweet my newest twitter updates. I’ve been looking for a plug-in like this for quite some time and was hoping maybe you would have some experience with something like this. Please let me know if you run into anything. I truly enjoy reading your blog and I look forward to your new updates.

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  198. Hello! This is kind of off topic but I need some guidance from an established blog. Is it difficult to set up your own blog? I’m not very techincal but I can figure things out pretty quick. I’m thinking about creating my own but I’m not sure where to begin. Do you have any ideas or suggestions? Many thanks

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  206. Hi there! I know this is somewhat off topic but I was wondering if you knew where I could find a captcha plugin for my comment form? I’m using the same blog platform as yours and I’m having problems finding one? Thanks a lot!

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  226. My developer is trying to persuade me to move to .net from PHP. I have always disliked the idea because of the expenses. But he’s tryiong none the less. I’ve been using WordPress on various websites for about a year and am nervous about switching to another platform. I have heard fantastic things about blogengine.net. Is there a way I can transfer all my wordpress posts into it? Any help would be really appreciated!

  228. Hello would you mind sharing which blog platform you’re working with? I’m looking to start my own blog in the near future but I’m having a difficult time deciding between BlogEngine/Wordpress/B2evolution and Drupal. The reason I ask is because your layout seems different then most blogs and I’m looking for something completely unique. P.S Sorry for getting off-topic but I had to ask!

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  244. I truly love your site.. Pleasant colors & theme. Did you make this site yourself? Please reply back as I’m planning to create my own blog and would like to know where you got this from or exactly what the theme is called. Thanks!

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  250. I truly love your website.. Excellent colors & theme. Did you build this website yourself? Please reply back as I’m looking to create my own website and would love to learn where you got this from or exactly what the theme is named. Thanks!

  254. Hey there this is kind of of off topic but I was wanting to know if blogs use WYSIWYG editors or if you have to manually code with HTML. I’m starting a blog soon but have no coding skills so I wanted to get guidance from someone with experience. Any help would be greatly appreciated!

  262. Howdy! This is kind of off topic but I need some help from an established blog. Is it difficult to set up your own blog? I’m not very techincal but I can figure things out pretty quick. I’m thinking about creating my own but I’m not sure where to begin. Do you have any tips or suggestions? Appreciate it

  266. I was wondering if you ever thought of changing the page layout of your blog? Its very well written; I love what youve got to say. But maybe you could a little more in the way of content so people could connect with it better. Youve got an awful lot of text for only having one or two images. Maybe you could space it out better?

  267. With havin so much written content do you ever run into any problems of plagorism or copyright violation? My site has a lot of unique content I’ve either created myself or outsourced but it seems a lot of it is popping it up all over the web without my permission. Do you know any solutions to help stop content from being ripped off? I’d certainly appreciate it.

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  286. Howdy! I know this is somewhat off topic but I was wondering which blog platform are you using for this website? I’m getting fed up of WordPress because I’ve had problems with hackers and I’m looking at alternatives for another platform. I would be awesome if you could point me in the direction of a good platform.

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  304. Hey! Quick question that’s completely off topic. Do you know how to make your site mobile friendly? My weblog looks weird when browsing from my iphone4. I’m trying to find a theme or plugin that might be able to correct this issue. If you have any recommendations, please share. Thanks!

  306. Howdy great blog! Does running a blog like this take a massive amount work? I have very little knowledge of computer programming but I had been hoping to start my own blog in the near future. Anyhow, if you have any suggestions or tips for new blog owners please share. I know this is off subject however I simply needed to ask. Many thanks!

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  310. I know this if off topic but I’m looking into starting my own weblog and was wondering what all is needed to get setup? I’m assuming having a blog like yours would cost a pretty penny? I’m not very web savvy so I’m not 100% positive. Any recommendations or advice would be greatly appreciated. Many thanks

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