Nfa to regular grammar

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Nfa to regular grammar

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If we read an a from state Awe go to the state B.

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But I don't know what that single a means in the first rule? From state B, if we read a bwe go to state A. But again, what does this single b mean in this rule? If we follow that, we get this automaton :. EDIT : As rici said, if we apply subset construction to the last automaton, we get this one : without dead states. Sign up to join this community.

The best answers are voted up and rise to the top. Asked 2 years, 10 months ago. Active 2 years, 10 months ago. Viewed 3k times. Active Oldest Votes.

Regular Expressions, Regular Grammar and Regular Languages

What do you get, if not the last automaton? I'll edit my answer. Thank you.

nfa to regular grammar

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I'm going over some problems from an old book and it asks you to find a regular grammar for the pictured NFA. I understand regular grammar when presented to me, but find it hard to place together all the possible scenarios without forgetting some. I know its not correct but i'm stuck on how to start building the grammar from scratch.

Can anyone help define some steps to take to solve the problem? One set of productions that will do this is:. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Asked 6 years, 10 months ago. Active 6 years, 10 months ago. Viewed times. Rev Rev 11 1 1 bronze badge.

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nfa to regular grammar

It only takes a minute to sign up. Then I came across many examples that claimed to use these rules to prepare regular grammars from given regex. However I was not able to understand how they are actually using these rules, as they directly gave final regular grammar for given regex.

So I decided to try some examples step by step and find whats going on. At each step, same color is used to match part of regex getting translated into corresponding part in grammar. Apart from star closure, there are many stuff that I dont find straight forward or at least requiring extra awareness that cannot be easily put in step-by-step procedure while preparing grammar. Other facts I should be aware of:.

Convert DFA NFA to Regular Expression - 083

I observed many more such small points which all I need to be aware at each step of preparing grammar. It makes me feel fuzzy.

Am I going correct with this at all? Is there any book which discuss regex to regular grammar direct conversion, giving clear step by step procedure?

Or there is simply no such procedure and I am unnecessarily trying to make it up from examples? As briefly indicated by Raphael in a comment, the only difference between an NFA and a linear grammar is formatting. You can use any algorithm which converts a regular expression to an NFA, and produce a right or left linear grammar instead of the NFA, simply by changing the way you produce output.

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Any correct regular expression to linear grammar algorithm will be some version of the above procedure since you could produce the transition table instead of the grammar by once again changing the print format. Sign up to join this community. The best answers are voted up and rise to the top. Steps to convert regular expressions directly to regular grammars and vice versa Ask Question.

Asked 3 years, 9 months ago. Active 1 year, 5 months ago. Viewed 21k times. Other facts I should be aware of: While preparing RLG, I should start from left of the regex While preparing LLG, I should start from right of the regex I observed many more such small points which all I need to be aware at each step of preparing grammar. Maha Maha 1, 4 4 gold badges 22 22 silver badges 39 39 bronze badges. I know books have discussed procedure for NFA to regular expression conversion but not above direct procedure.Introduction Converting to a Regular Grammar.

The reader, if he or she hasn't already, should read the tutorial about creating a finite automatonwhich covers the basics of constructing a FA and describes how they are implemented in JFLAP. This section specifically describes how one may transform one of these finite automata into a right-linear grammar.

Then, either load the file dfaToRegGrammar. When finished, your screen should look something like this:. Converting to a Regular Grammar. We will now convert this DFA into a regular grammar.

Notice the labels on the states in the picture. JFLAP, by default, assigns unique variables to each state. Each transition in the graph corresponds with a production in a right-linear grammar.

nfa to regular grammar

Let's add this production to our list of productions in the right panel. Now, let's see what our next step might be. Now, how many productions do we still need to generate. After finishing, the following should be your list of productions even if not exactly in that order :. This concludes our brief tutorial on converting FAs into regular right-linear grammars.

Thanks for reading!As discussed in Chomsky HierarchyRegular Languages are the most restricted types of languages and are accepted by finite automata. Regular Expressions Regular Expressions are used to denote regular languages. An expression is regular if:. Regular Languages : A language is regular if it can be expressed in terms of regular expression.

L2 will also be regular. Complement of a language can be found by subtracting strings which are in L G from all possible strings. D The set of all strings that begin and end with either 0 or 1. Solution : Option A says that it must have substring But is also a part of language but it does not contain 00 as substring.

So it is not correct option. Option C says that it must contain atleast two 0. In regular expression, two 0 are present. So this is correct option.

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Option D says that it contains all strings that begin and end with either 0 or 1. But it can generate strings which start with 0 and end with 1 or vice versa as well.

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So it is not correct. Question 2 : Which of the following languages is generated by given grammar? Solution : Option A says that it will have 0 or more a followed by 0 or more b.

So A is not correct. Option B says that it will have equal no. So B is not correct. But as shown in option Aba is also part of language. So C is not correct. So D is correct.We will let each state in the NFA correspond to a non-terminal in the grammar. Each symbol used on the transitions corresponds to a terminal symbol. This process will work equally well with a DFA, and can be applied in reverse to a regular grammar to produce the corresponding NFA.

Let S be the start symbol in G'. Create a Accepting state F 4. We have seen that the regular languages are closed under common set-theoretic operations; the same, however, does not hold true for context-free languages. Lemma: The context-free languages are closed under union, concatenation and Kleene closure.

Proof: We will prove that the languages are closed by creating the appropriate grammars. Suppose we have two context-free languages, represented by grammars with start symbols.

First of all, rename all the terminal symbols in the second grammar so that they don't conflict with those in the first. Proof: We will prove the non-closure of intersection by exhibiting a counter-example. Consider the following two languages:.Play the show parlay by yourself or with your friends.

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nfa to regular grammar

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