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Concatenation of two non regular languages

In theoretical computer science and formal language theorya regular language also called a rational language [1] [2] is a formal language that can be expressed using a regular expressionin the strict sense of the latter notion used in theoretical computer science as opposed to many regular expressions engines provided by modern programming languages, which are augmented with features that allow recognition of languages that cannot be expressed by a classic regular expression. Alternatively, a regular language can be defined as a language recognized by a finite automaton.

The equivalence of regular expressions and finite automata is known as Kleene's theorem [3] after American mathematician Stephen Cole Kleene. In the Chomsky hierarchyregular languages are defined to be the languages that are generated by Type-3 grammars regular grammars.

concatenation of two non regular languages

Regular languages are very useful in input parsing and programming language design. See regular expression for its syntax and semantics. Note that the above cases are in effect the defining rules of regular expression.

Techniques to prove this fact rigorously are given below.

concatenation of two non regular languages

Properties 9. In this case, equivalence over M leads to the concept of a recognizable language.

concatenation of two non regular languages

Some authors use one of the above properties different from "1. Some of the equivalences above, particularly those among the first four formalisms, are called Kleene's theorem in textbooks.

Precisely which one or which subset is called such varies between authors. One textbook calls the equivalence of regular expressions and NFAs "1. The regular languages are closed under various operations, that is, if the languages K and L are regular, so is the result of the following operations:. Given two deterministic finite automata A and Bit is decidable whether they accept the same language. For regular expressions, the universality problem is NP-complete already for a singleton alphabet.

In practice, most nonregular problems are solved by machines taking at least logarithmic space. To locate the regular languages in the Chomsky hierarchyone notices that every regular language is context-free. The converse is not true: for example the language consisting of all strings having the same number of a 's as b 's is context-free but not regular. To prove that a language such as this is not regular, one often uses the Myhill—Nerode theorem or the pumping lemma among other methods.

The ordinary generating function for L is the formal power series. The generating function of a language L is a rational function if L is regular.

Consider, for example, the Dyck language of strings of balanced parentheses. The zeta function of a language L is [26]. The zeta function of a regular language is not in general rational, but that of an arbitrary cyclic language is.

Likewise, the notion of a recognizable language by a finite automaton has namesake as recognizable set over a monoid that is not necessarily free. Papers influenced by Eilenberg 's monograph [34] often use either the term "recognizable language", which refers to the behavior of automata, or "rational language", which refers to important analogies between regular expressions and rational power series.

In fact, Eilenberg defines rational and recognizable subsets of arbitrary monoids; the two notions do not, in general, coincide. This terminology, while better motivated, never really caught on, and "regular language" is used almost universally. Rational series is another generalization, this time in the context of a formal power series over a semiring. This approach gives rise to weighted rational expressions and weighted automata.

08 12 non regular languages

In this algebraic context, the regular languages corresponding to Boolean -weighted rational expressions are usually called rational languages. From Wikipedia, the free encyclopedia. Formal language that can be expressed using a regular expression. For natural language that is regulated, see List of language regulators. For his theorems for recursive functions, see Kleene's recursion theorem. Main article: Induction of regular languages.

Algebraic automata theory.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The dark mode beta is finally here.

Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. Note: For concatenation of two language must be regularthere has to be atleast one language to be regular. So, we can say the union of two always results in context-free language. Take the above example again:. Check this out: Geeks for Geeks. Learn more. Asked 6 years, 2 months ago. Active 7 months ago. Viewed 4k times. Given L1 context free non regular language.

Given L2 regular language. I think that the 2nd one is impossible. But I'm not sure. Njol 2, 12 12 silver badges 30 30 bronze badges. Rouki Rouki 2, 17 17 silver badges 32 32 bronze badges.

Active Oldest Votes. Yes, Possible. Grijesh Chauhan Grijesh Chauhan Rouki I have already answered this here Why the need for terminals?

Is my solution sufficient enough?

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You have to prove that the concatenation is regular for every possible pair of languages, not just two of your choice. Yes, it is possible. Genius Genius 2 2 silver badges 9 9 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. Podcast Programming tutorials can be a real drag.

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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. If such a proof is correct, then two more questions arise: Are there countably infinite amount of such examples which the concatenation pf two non-regular languages is a regular language?

Are there uncountably infinite amount of such examples? A finite cross product of countably infinite sets is countably infinite. Thus, there are countably infinite amount of such examples. The infinite cross product of all these countably infinite sets is uncountably infinite. Thus, there are uncountably infinite amount of such examples. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered.

Are there two non-regular languages whose concatenation is regular? Ask Question. Asked 5 years, 1 month ago. Active 5 years ago. Viewed 6k times. Are my proofs right? Is there easier way to prove these questions? Pin 25k 2 2 gold badges 21 21 silver badges 64 64 bronze badges. Scott Mar 18 '15 at What about the rest of the prove?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. Will L. M concatenation be a regular language? Please explain your answer and if yes then what will be its expression? Regular languages are precisely those languages that are recognized by some nfa.

Just use the equivalence with regular expressions. More generally, the product of two regular languages is regular. L2 is regular, it represents a language having any number of 0's followed by any number of 1's.

But, L1. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Concatenation of regular languages [closed] Ask Question. Asked 6 years, 1 month ago. Active 6 years, 1 month ago.

concatenation of two non regular languages

Viewed 4k times. Thanks for any help in advance. David Richerby Mcolorz Mcolorz 11 1 1 silver badge 1 1 bronze badge. I am sorry for that.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. Sign up to join this community.

The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Can the concatenation of two non-regular languages be regular? Asked 4 years, 11 months ago. Active 4 years, 11 months ago. Viewed 2k times. Rick Decker David David 39 2 2 bronze badges. What are your thoughts? Where did you get stuck? We want to help you understand, not do your exercise for you, and we expect you to make a serious effort on your own before asking. What non-regular languages do you know?

Active Oldest Votes. The Overflow Blog. Socializing with co-workers while social distancing. Featured on Meta. Community and Moderator guidelines for escalating issues via new response…. Feedback on Q2 Community Roadmap. Towards a policy for questions about contest problems.

Linked Related 1. Hot Network Questions.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The dark mode beta is finally here. Change your preferences any time.

Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. Will L. M concatenation be a regular language? Please explain your answer and if yes then what will be its expression? Learn more. Concatenation of regular languages [closed] Ask Question. Asked 6 years, 1 month ago.

Active 6 years, 1 month ago. Viewed times. Thanks for any help in advance. Mcolorz Mcolorz 1 1 gold badge 5 5 silver badges 17 17 bronze badges. This question appears to be off-topic because it belongs on cs.

Mcolorz, that is neither here or there. That language is not the concatenation of L and M. Mcolorz yes L.

Regular language

M is regular. Instead L. Active Oldest Votes. The Overflow Blog. Podcast Programming tutorials can be a real drag.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The dark mode beta is finally here. Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information.

Suppose that the two non-regular languages are distinct and have no strings in common. The intersection of these 2 languages will be the empty set, since no string exists in both languages. Suppose L and L' are non-regular languages.

Can we conclude that L intersection L' is not regular? The answer to this question can be found here. Learn more. Can the intersection of 2 non-regular languages be a regular language? Ask Question. Asked 5 years ago. Active 5 years ago. Viewed 4k times. Asmae Asmae 33 1 1 silver badge 3 3 bronze badges.

I think you'll need to be more specific. I can't see why it couldn't be. You could have a left-field OO language "crossed" with a functional language, and end up with something like Scala. This is not what is meant by "regular" and "non-regular" languages. Active Oldest Votes. The empty set is a regular language, so this can happen sometimes. Thank you very muchthis was the most simple answer.

What about the union? No problem. Sometimes it's not obvious what will turn out to be a counterexample and what won't. I believe it can be either regular or non-regular. Reynaldo Aguilar Reynaldo Aguilar 1, 11 11 silver badges 27 27 bronze badges. Thank you very much! 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.

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