- Construction of an FA from an RE
- Regular expression to ∈-NFA
- Regular Expression to NFA
- Converting Regular Expression to NFA
- CFG to PDA Conversion

## Construction of an FA from an RE

NFAs are useful to show regular languages are closed under the last three operations union, concatenation, star. A Generalized Nondeterministic Finite Automaton is similar to an NFA but the transition function takes a state and a regular expression in the alphabet instead of a state and an alphabet element. The idea is that in state q 0 the transition to state q 1 can be taken if the next input matches the regular expression Note that there is only one accept state. However, this is no real restriction for a nondetrministic automaton. On the other hand, the transition function is defined on a different arguments than is the case for an ordinary NFA. The definition of the language of a GNFA is technically different than that of an NFA because the transition function is defined differently. However, the idea is really similar, but extended to allow regular expressions on the transitions. Steps 1 and 2 require adding a new start state and a new accepting state. Step 3 require no changes in the diagram except labeling the transitions out of the new start state and into the new accepting state. There are 3 arrows coming into state q 1 from other states: q 0q 2and q 4. To show the first part, if we are given an DFA, we need to show that there is a regular expression that describes exactly the language of the DFA. The construction of the regular expression begins with the DFA and each step will eliminate one state of the DFA until the only state s remaining are the start state and a final state. To show that for any regular expression there is an NFA that recognizes the same language described by the regular expression, the proof describes a procedure for constructing the NFA from the regular expression. What is L3 o L4 concatenation? For example, to eliminate state q 1 in replace each existing path q to q 1 to q ' by a path from q to q ' Label the new path with a regular expression that describes the strings that would cause a transition from state q to q 1 to q ' There are 3 arrows coming into state q 1 from other states: q 0q 2and q 4. If state q 1 is removed, paths must be replaced by new transitions: q 0 to q 2 q 2 to q 2 q 4 to q 2. Eliminating q 1what regular expressions are needed? Convert this DFA to a regular expression that describes the same language. Parse the regular expression into its parts based on the regular expression operator precedence and parentheses used if any to determine the operands of each operator. For each of the operators use the construction described in showing the closure properties of regular languages to construct an NFA for each operator and its operands.## Regular expression to ∈-NFA

By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. To build a DFA using derivatives, we'll have states labeled with REs as above, the RE matches words which start at that state and end at an accept state. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Ask Question. Asked 5 years, 5 months ago. Active 3 years, 11 months ago. Viewed times. Active Oldest Votes. Brian M. Scott Brian M. Scott k 43 43 gold badges silver badges bronze badges. Tad Tad 5, 1 1 gold badge 9 9 silver badges 25 25 bronze badges. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. The Overflow Blog. Q2 Community Roadmap. Featured on Meta. Community and Moderator guidelines for escalating issues via new response…. Feedback on Q2 Community Roadmap. Autofilters for Hot Network Questions. Related 0.

## Regular Expression to NFA

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## Converting Regular Expression to NFA

By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. It only takes a minute to sign up. So I've been trying to crack this for a long time and almost feel like I am going in loops about this question. I understand that you would have the following for the first step adding empty states :. The next step would be removing the state [q1] I would get:. Finally removing [q2] would get:. A GNFA generalised nondeterministic finite automaton is described as follows:. When contructing a regular expression there is no unique correct answer. There are usually several expressions "that make sense". In this case you use state elimination method I learned this under the name of Brzozowski and McCluskey. Here the order of removal determines the expression found. You can also do "clever tricks" during the construction. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Ask Question. Asked 6 years, 11 months ago. Active 4 years, 3 months ago. Viewed 17k times.

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