# Questions tagged [regular-languages]

Questions about properties of the class of regular languages and individual languages.

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### How to prove this language is not regular?

I am currently learning Pumping Lemma and found this question. But I am not able to prove it not regular. L = { $0^n$ | n is power of 2}. So, here I considered w = $0^{2^n}$ where n is constant of ...
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### DFA, lower bound on number of states, language with primes and remainders

This is an exercise from old exam on formal languages that I don't know how to solve: Let $p \ge 5$ be a prime number and $L_p$ be a language of words over $\{0,1\}$ that read in binary from right (i....
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### How to characterize equivalence classes induced by Myhill-Nerode theorem?

Given $L=\lbrace w\in \lbrace 0,1 \rbrace^\ast : N_0(w)=N_1(w) \rbrace$, where $N_0(\cdot)$ and $N_1(\cdot)$ mean the number of zeroes and ones respectively, I need to characterize the classes ...
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### Time Complexity of Regular Languages

I wonder how I can go about proving that if a language L is decidable in o(nlog(n)) then L must be regular. I should probably mention that by "decidable" I mean "being decidable by single-tape ...
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### Prefix/suffix property of language containing only empty word

Does language $L ={\varepsilon}$, where $\varepsilon$ - empty word has suffix/prefix property? The definition says that language has prefix/suffix property requires that there is no code word in the ...
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### Meaning of L* if L is a language

I can't find anywhere the meaning of $L^*$, given that $L$ is a language. I know $^*$ means repetition, for example $0^*$ = $\{ \epsilon, 0, 00, 000, \dots \}$. Or if $A$ is an alphabet $A^*$ are all ...
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### Can the regular image of a context-free language be undecidable?

I just need to know the truth or falsity of a simple statement. Let $L_1$ be a context-free language over an alphabet which contains some number of characters $\Sigma$, as well as a single, special ...
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### Converse of pumping lemma for regular expressions

I want to come up with a language that satisfies the pumping lemma while not being a regular expression. I thought of $\{0^i1^j: i > j > 0\}$. The pumping seems to work just fine, and this is ...
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### How can I find the Myhill-Nerode classes for the language A?

I have the following task (no homework). Find all equivalence classes of the Myhill-Nerode relation of the language $$\mathrm{A} \triangleq\{w \in \Sigma^{*} | w\text{ does not end with }01\}\,.$$...
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### regular expression with kleene closure [duplicate]

my question is if my regular expression R is 1* that means the language accepted is {^,1,11,111,1111...} in that case i don't understand the meaning what (R*)* means
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### Counting number of states from a regular expression

Given the regular expression: $r=ab+((a+\epsilon)c^*)^*$. Let A be a non-deterministic automaton that accepts the language of r. How many states are in A? Answer the question without building A ...
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### Finding a regular expression of a language

Our alphabet is {a,b} and we need to find a regular expression for the language of all words of the form $a^*b^*$, whose length is a multiple of 3. Obviously $(aaa)^*(bbb)^*$ is one of the options, ...