The tag has no wiki summary.

learn more… | top users | synonyms

0
votes
2answers
40 views

Are those two regular languages the same?

Given an alphabet of {a,b} where Na denotes the number of occurrences of a, and Nb the number of occurrences of b: ...
1
vote
1answer
159 views

Pumping lemma $L=\{a^ib^j | i \neq j ; i,j \ge 0\}$ [duplicate]

So, let's have language $L=\{a^ib^j | i \neq j ; i,j \ge 0\}$ I have to prove that it's not regular. \begin{align} \omega=a^nb^{n+1}=a^{n-1}ab^{n+1} \end{align} \begin{align} x&=a^k\\ y&=a\\ ...
1
vote
2answers
133 views

interpreting language for finite state machine

Can someone explain to me what this means in clear english and maybe give me a hint for how to make a NDFSM (non-deterministic finite state machine) that accepts this language? I understand that the 3 ...
1
vote
1answer
105 views

Constructing a parallel composition from a given transition system and automaton

I am looking at an exercise, where it asks me to construct a parallel composition from a given transition system and an automaton. The transition system looks like this: and the automaton (with ...
4
votes
2answers
120 views

Number of states required to recognize $\{ ss : s \in \{ 0 , 1 \}^*, |s| = i \}$ and its complement

$$\Sigma = \{0,1\}\;\\ S_{i} = \left\{ss: s\in {\Sigma}^{*} \text{and $s$ has length $i$}\right\}$$ Prove that for any $i$, any DFA recognizing $S_{i}$ must have $2^{i}$ or more states. Design a ...
10
votes
2answers
111 views

Mystery Men Movie - Propositional Logic

In the movie Mystery Men, there is this scene: Captain Amazing (good guy): I knew you couldn't change. Casanova Frankenstein (bad guy): I knew you'd know that. Captain Amazing: Oh, I know. And ...
2
votes
1answer
205 views

A variation on counting Balanced Brackets

While counting the number of balanced bracket expressions of length $2n$, the constraint is that for every prefix substring: $$\text{[number of occurrences of (]} - \text{[number of occurrences of )]} ...
0
votes
1answer
365 views

Does closure under the union and concatenation operations imply closure under the star operation?

Given any two languages $A$ and $B$, recall the following regular operations: Union: $A \cup B = \{x \mid x \in A \text{ or } x \in B\}$ Concatenation: $A \circ B = \{xy \mid x \in A \text{ ...
1
vote
2answers
335 views

Constructing a finite automata from a subset of its language

I am attempting to solve the following problem: Let $M=(Q,\Sigma,\delta,q_0,F)$ be a deterministic finite automata which accepts $L(M)$, and let $E$ be the subset of $L(M)$ consisting of all words of ...
1
vote
2answers
84 views

The Relation of Cellular Automata to Languages

In Conway's Game of Life, would a cell be considered a deterministic finite automata? Is there a language for the automata, and would it be a regular language? In probabilistic cellular automata, are ...
0
votes
1answer
58 views

Connection of closed subsets of $A^{\omega}$ and deterministic Büchi-Automata, Question from Book: Infinite Word by D. Perrin & J.-E. Pin

In the Book Infinite Words (homepage) it is proofed that: If $X \subseteq A^{\omega}$, then regarding the Cantor-Topology, the following is equivalent: (1) $X$ is closed (2) $X$ is recognized by a ...
2
votes
1answer
65 views

Is there an (explicit?) bijection from the set of all automatons to the set of all regular expressions that conserves the recongnised language

Let $\Sigma$ be an alphabet, $R$ be the set of regular expressions on $\Sigma$ (that is, trees with leave's values in $\left\{\varepsilon\right\}\cup \Sigma$ and three types of interior nodes, one ...
0
votes
1answer
231 views

Question on NP and its closure properties

Is this true or false? If $L_1$∈ NP and $L_2$∈ NP, then $L_1$∩ $L_2$ ∈ NP. NP = nondeterministic polynomial
1
vote
2answers
69 views

Trying to describe this Turing Machine

Let's say I have the following turing machine: $F_n$ = {M | M is a TM and |L(M) ≤ n} In english, for some given natural number n, $F_n$ is the language of all turing machines that accept no more ...
0
votes
1answer
73 views

Need help with this regular language proof

I'm trying to prove that if $L$ is regular, then $L_S$ is regular as well. $L_s$ = {$x$ | $∃$ $w ∈ Σ^*$ such that $wx∈L$} I know one way to do this would be to create an NFA that accepts $L$, then ...
2
votes
0answers
56 views

Expressiveness of finite memory programs

Assume we have a simple programming language with while, if, := (assignment), ...
3
votes
1answer
231 views

Formal Reduction: Pushdown Automata recognizing context free languages with bounded stack

I am studying for an exam in automata theory and I am having trouble solving the following: Consider pushdown automata and context free languages. Show that the following decision problem is ...
1
vote
0answers
52 views

Systematic way of creating the complement of a regular grammar?

Regular languages are closed under complement. And any regular language can be generated using a regular grammar. Is there a systematic way to create the rewrite rules for the complement of a regular ...
8
votes
5answers
464 views

A computer's memory is finite, so how can there be languages more powerful than regular?

A computer has a finite memory. There are no computers with infinite memory. Therefore the only languages that a computer can process are those whose member strings are finite. As I recall, the ...
2
votes
1answer
118 views

Why do complex grammars require powerful algorithms?

I am reading a fabulous book on Formal Languages and in the book it says: As the rewrite rules of a grammar become more complex, the algorithm for recognizing the associated language becomes ...
1
vote
0answers
43 views

Regular Functional Algorithms

A language is regular if it is accepted by a read-only Turing machine. I am curious about applying this model to functional problems rather than decision problems. Definition: A functional read-only ...
1
vote
1answer
84 views

Proving a language is not regular using pumping lemma

I had an exam today and the professor gave us the following problem: Let $L = \{a^nb^m : n|2m \}$. Prove that $L$ is not regular. Ok this sounds easy. Here is my solution: Assume opposite -- $L$ is ...
0
votes
1answer
157 views

Is this language regular?

Given $m,n∈Z$, A is a finite alphabet set ,and $L=\{(a^m,a^n)\}^*$ is subset of $A^*\times A^*$ . Is this language regular ? For example, is $L=\{(a^3,a^7)\}^*$ regular ? Here L is not the set ...
2
votes
2answers
52 views

Regular composition of non-regular language

I've got the following problem: Let's take language $L$. Is it posible that $L$ is not regular itself, but it's composition $L\cdot L$ becomes regular? I suspect that's correct, yet I ...
0
votes
1answer
99 views

Pumping Lemma Proof for $ww$

The proof of language $F = \{ww\mid w ∈ \{0,1\}^*\}$ is not a regular language using pumping lemma most of the solutions i found uses the string $0^p10^p1$. I understand the proof using that. But in ...
4
votes
2answers
86 views

Prove that $\{1, 11, 1001,\dots\}$ is an irregular language

Let $L:=\{1, 11, 1001,\dots\}$ be the language with alphabet $\{0,1\}$ which is formed by all powers $3^n, n=0,1,\dots$ written in binary notation. How to prove that $L$ is not regular?
1
vote
1answer
96 views

Give a regular grammar for L

Give a regular grammar for L= {a^n b^n : n<=100} I would do something like this : S---> A | empty string A---> aB| empty String B---> Ab but How do we keep count of the number in the grammar? ...
3
votes
0answers
831 views

Pumping lemma for $a^nb^{2n+1}$

I know how to solve pumping lemma for $a^nb^n:n\geq 0$. But I don't understand how can I solve this example : $a^nb^{2n+1}:n\geq 0$. I tried to solve it but I am not sure that I have solved it ...
0
votes
2answers
159 views

Prove $L=\{ 1^n| n\hspace{2mm}\text{is a prime number} \}$ is not regular.

Prove $L=\{ 1^n| n\hspace{2mm}\text{is a prime number} \}$ is not regular. It seems to use one Lemma: Pumping Lemma.
3
votes
2answers
2k views

Are regular languages necessarily deterministic context-free languages?

The original problem Suppose M is DCFL (Deterministic Context Free Language) and N is a regular language. Answer the following questions and justify your answers. a) Is M-N necessarily context-free? ...
2
votes
2answers
53 views

If $\{w^k|w\in L\}$ regular implies L regular?

If L is a language and the language $$\tilde{L}:=\{x^k,x\in L, k\in\mathbb{N}\}$$ is regular, does that imply that L is regular? ($|L|<\infty$ gives equivalence) We came across this question when ...
1
vote
2answers
39 views

Proving irregularity of a language

While learning about formal languages, I found the following problem: Let us consider words over the alphabet $\lbrace 0, 1\rbrace ^3$. We say that a word $\langle a_1, b_1, c_1 \rangle \ldots ...
0
votes
1answer
83 views

Algorithm for checking if regular language has given property

Give an algorithm that will decide (in any finite time) if given regular language $L$ (given by some regular expression) has given property: $$\forall_{x\in L} \exists_{y\in L} \left( \left(x\neq ...
1
vote
0answers
63 views

Proving that language is regular or not regular

Let $L$ be a regular language. Prove that: $L_{+--}=\left\{w: \exists_u |u|=2|w| \wedge wu\in L\right\}$ $L_{++-}=\left\{w: \exists_u 2|u|=|w| \wedge wu\in L \right\}$ ...
3
votes
2answers
105 views

Is $\frac12 L$ a regular language?

Let $L$ be a regular language. Is $\frac{1}{2}L := \left\{ w: \exists_u |u|=|w| \wedge wu\in L \right\}$ regular too? I think the answer is YES. But I don't know how to prove it. I was trying to ...
1
vote
1answer
98 views

Is language of binary representations regular?

Let $bin(n)$ denote binary representation of an integer $n$. Let $L=\left\{bin(n^2):n\in\mathbb{N}\right\}$. Is $L$ a regular language?
1
vote
1answer
67 views

How to prove that given language is not regular?

Prove that $$L=\left\{uvvw\mid u,v,w \in \{a,b,c\}^*\text{ and }v\ne\varepsilon\right\}$$ is not regular a regular language.
1
vote
2answers
148 views

Infinite union of finite unions

Is the following sound reasoning, and if so, why? Letting $S$ be a language over the alphabet $\Sigma$, $$ \bigcup_{i=0}^{\infty}\left(\bigcup_{k=0}^{i-1}S^k\right) = \bigcup_{i=0}^{\infty}S^i $$
0
votes
0answers
133 views

Chomsky Normal Form solution for a problem

Here is my attempt at CNF, Original: $$ \begin{align*} S &\to 1 A \mid O B \\ A &\to O B O \mid 1 0 \mid \epsilon \\ B &\to A 1 A \mid 0 1 \end{align*} $$ CNF: $$ \begin{align*} S ...
2
votes
2answers
99 views

Giving a regular grammar for the language

I am trying to brush up on my regular grammar knowledge to prepare for an interview, and I just am not able to solve this problem at all. This is NOT for homework, it is merely me trying to solve ...
2
votes
1answer
119 views

Pumping Lemma problem

Apply pumping lemma to each of these and prove that they are not regular. $L = \{ (0^p)(1^q)2 \mid 0 < q < p\}$ $L_2 = \{ (a^p)(b^q)(c^r) \mid p = q \text{ or } q = r\}$ Here my ...
0
votes
2answers
105 views

Regular expression for strings with length not a multiple of 10

Let $P = \{z^n \mid \text{$n$ is not divisible by $10$} \}$. Give a regular expression for this language and then a generalized regular expression that is shorter than the regular expression.
2
votes
1answer
83 views

Is there a problem with this example?

In example $1.14$ on page $51$ (of the book and $64$ of this link), shouldn't the string $01000$ get rejected? However it seems that the first three digits of the string would force it to an accept ...
3
votes
1answer
152 views

Does the Halting Problem apply when evaluating programs that are regular languages?

Here is my understanding of the Halting Problem: It is impossible to write a program H that can determine for any arbitrary program ...
1
vote
2answers
355 views

If $L$ is regular, prove that $\sqrt{L}=\left\{ w : ww\in L\right\}$ is regular

Let $L$ be a regular language. Prove that $\sqrt{L}:=\left\{ w : ww\in L\right\}$ is also a regular language. I suppose I need to modify state machine for $L$ to accept $\sqrt{L}$, but I've been ...
3
votes
2answers
139 views

Is this proof using the pumping lemma correct?

I have this proof and it goes like this: We have a language $L = \{\text{w element of } \{0,1\}^* \mid w = (00)^n1^m \text{ for } n > m \}$. Then, the following proof is given: There is a $p$ ...
2
votes
2answers
325 views

Regular Languages Algorithm?

I need help proving the following question: Let $L$ be any regular language on $\sum{a,b}$. Show that an algorithm exists for determining if L contains any strings of even length. So far, I know ...
1
vote
1answer
211 views

Prove that if $ L $ is a regular language over the alphabet $ Z = \{ 0,1 \} $, then $ L' = \{ax \mid x \in L \} $ is also regular for any a in $Z$.

Prove that if $L$ is a regular language over the alphabet $Z = \{0,1\}$, then $L' = \{ax \mid x \in L\}$ is also regular for any $a \in Z$. I'm not sure how to even begin on this one. If even a ...
3
votes
2answers
95 views

If $L\in REG$ then $M$ has a finite number of distinct rows

Let $L \subseteq \Sigma^{\star}$ and let $M^{\Sigma^{\star} \times \Sigma^{\star}}(\{0,1\})$ an infinite matrix such that for each $x,y\in \Sigma^\star$: $$ m_{x,y}=\begin{cases} 1 & x y\in L\\ 0 ...
2
votes
1answer
93 views

Is $L = \{a^{n+2} b^n | n \ge 0\}$ context free or regular?

Is the language $L = \{ a^{n+2} b^n | n \ge 0 \}$ context free? If so, what is a context free grammar for it? If it is regular, what is a right linear grammar for it?