Questions related to formal languages, grammars, and automata theory

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0
votes
1answer
41 views

Union of finite and non-regular language [duplicate]

Question: ($B$ and $C$ are languages) $B$ is finite,$C$ isn't regular: Prove/Disprove: $C\cup B$ isn't regular. Thoughts: My intuition says this is true, but I need an idea to prove it. Since I ...
4
votes
1answer
779 views

How to show that L = L(G)?

Specifying formal languages by giving formal grammars is a frequent task: we need grammars not only to describe languages, but also to parse them, or even do proper science. In all cases, it is ...
2
votes
0answers
8 views

Tightest upper bound on length of distinguishing string in Hopcroft's algorithm

Hopcroft's algorithm is an algorithm for DFA minimization that produces a table identifying which pairs of states are distinguishable. What is the tightest possible upper bound (with proof) on the ...
0
votes
1answer
79 views

What is meant by the notation $L(…)$?

I am currently studying about formal languages and automata. I am trying to solve a problem but there is a notation whose meaning I'm not sure of. I have a question to find out the relationship ...
-1
votes
1answer
93 views

DFA for every run of a's=2 or 3

I am trying to create a dfa for L={w: every run of a's has length either two or three} this is my attempt at the solution..i feel like I am missing something..?
0
votes
0answers
24 views

What is the procedure for converting this finite automaton into a regular expression? [duplicate]

Could someone provide an explanation of how to convert this DFA into a regular expression? I have found three methods online, ie: How to convert finite automata to regular expressions? but they are ...
0
votes
0answers
15 views

non-regular context free language with logarithmic stack usage [duplicate]

Can you suggest a context-free language $L$, which is: non-regular has a PDA which accepts all $w\in L$ and uses maximum stack space of $\log(|w|)$.
0
votes
0answers
25 views

Difference between Turing machine end state and halt

Is there a difference between the end state of a Turing machine and the halt state? Especially, for example the Busy Beaver 3. It is said that it is with 3 states but there is also a halt. Is the end ...
-2
votes
0answers
33 views

a question for formal language [on hold]

could anyone give me some examples of below set?? thanks in advance!! :) L1 = L((ab+ba)*) L2 = L(((a+b)b)*) L3 = L((a*+b*)*)
0
votes
1answer
49 views

What is the complement of empty language? [on hold]

Consider a turing machine that accepts the empty language. What will be the complement of the language generated by the above turing machine? A) Recursive B) Recursive Enumerable C) Non recursive ...
0
votes
1answer
33 views

closure property on languages

The above image, taken from planetmath.org, describes the closure property on REG (regular), DCFL (deterministic context-free), CFL (context-free), CSL (context-sensitive), RC (recursive), RE ...
-1
votes
0answers
31 views

Theory languages question [closed]

This is a question from theory of computation by C Martin If $L_1$,$L_2$, and $L_3$ are languages are the following languages equal? $L_1 (L_2 \cap L_3)= L_1 L_2 \cap L_1 L_3$ These language are ...
0
votes
1answer
48 views

Three languages and how to decide if they are regular

From following languages which one is regular and why others are not?And what is the regular expression for regular one. $L_1= \{wxwy | x,y,w \in (a+b)^+\}$ $L_2 = \{xwyw | x,y,w \in (a+b)^+\}$ ...
4
votes
0answers
45 views

Is there $L$ such that $L$ and $\bar L$ are context free, but $L$ is not deterministic context free?

The usual candidates for context free languages whose complement is also context free, but they are not regular are the Deterministic Context Free Languages ($DCFL$). For example, $L=\{a^nb^n\mid ...
2
votes
1answer
317 views

Reducing a non-RE language to its complement

Is there a language $L$ such that both $L$ and $L$'s complement are non turing recognizable languages, but there is a reduction between them? I couldn't find one...
7
votes
2answers
3k views

Intersection and union of a regular and a non-regular language

Let $L_1$ be regular, $L_1 \cap L_2$ regular, $L_2$ not regular. Show that $L_1 \cup L_2$ is not regular or give a counterexample. I tried this: Look at $L_1 \setminus (L_2 \cap L_1)$. This one ...
-1
votes
1answer
38 views

Create CFG and pushdown automaton for {ww} [duplicate]

I've been trying to make a CFG, a pushdown automaton and a regular expression for the language $\qquad L(M) = \{ww : w \in \{a, b\}^*, |w| \text{ is even}\}$. I understand how the reverse of the ...
2
votes
1answer
71 views

Language of binary strings divisible by 7

There was a question something like, "Consider the language of all integers converted to binary form. The language of all strings divisible by 7 is : 1) Recognizable by a finite-automaton. 2) ...
6
votes
1answer
917 views

Gödelization in Turing Machine

I was looking at Gödelization in Theory of Computation course. I could understand the Gödel numbering concepts, but couldn't understand its importance in Theory of Computation. Could anyone please ...
6
votes
2answers
402 views

Single-tape Turing Machines with write-protected input recognize only Regular Languages

Here is the problem: Prove that single-tape Turing Machines that cannot write on the portion of the tape containing the input string recognize only regular languages. My idea is to prove that this ...
7
votes
2answers
211 views

Counting the number of words accepted by an acyclic NFA

Let $M$ be an acyclic NFA. Since $M$ is acyclic, $L(M)$ is finite. Can we compute $|L(M)|$ in polynomial time? If not, can we approximate it? Note that the number of words is not the same as the ...
2
votes
2answers
55 views

Method for measuring the 'similarity' between FSA grammars?

I'm working with a pattern matching algorithm that generates an acyclic finite state automaton that accepts a given text string and all its substrings. The FSA algorithm is being run on a symbolic ...
3
votes
1answer
55 views

Creating a CFG that connects lengths of three blocks

I have to create a CFG which generates $$\{a^n (ab)^n c^m d^\ell e^k \mid n>0, k, \ell, m\ge0, k<m, m=\ell+k\}$$ The first part is easy enough, I came up with $$\begin{align*} S &\to ...
0
votes
1answer
76 views

Is Myhill-Nerode equivalence class of a language which contains all palindrome pairwise distinct?

In my formal language class, we define a language called PAL, which is on a alphabet set $\Sigma = \{0,1\}$. $PAL = \{w \in \{0,1\}^* : w = w^R\}$. We have proved that every string in this language ...
2
votes
3answers
113 views

How to generate a context sensitive grammar

I am trying to solve for my exam coming up and have no clue how to generate the grammar for Context sensitive languages for example how do i proceed on this kind of question. Give a context-sensitive ...
13
votes
1answer
398 views

Are context-free languages in $a^*b^*$ closed under complement?

The context-free languages are not closed under complement, we know that. As far as I understand, context-free languages that are a subset of $a^*b^*$ for some letters $a,b$ are closed under ...
-1
votes
2answers
73 views

Pushdown Automata: CFG to PDA

I have the following grammar for a context-free language: $G = (\{S,A,B\}, \{x,y,z\}, P, S)$ with $P = \{S \rightarrow A, A \rightarrow xAz, A \rightarrow xBz, B \rightarrow y\}$ My question is: How ...
0
votes
1answer
43 views

What context free grammar generates the language $L(G) = \{a^ib^jc^{2i}d^m\}$ [duplicate]

I am struggling to think of the context-free grammar that generates the language $L(G) = \{a^ib^jc^{2i}d^m\}$, where $i$, $j$ and $m$ are natural numbers. Also, in general, are there any good methods ...
4
votes
2answers
131 views

Gyorgy E. ReveszExercise 1.1: Show the grammar $G$ generates the language $L$ [duplicate]

The exercise says "Show that the grammar $G = \langle\{S\}, \{a, b\}, S, \{S \to \lambda, S \to aSb\}\rangle$ generates the language $L = \{a^i b^i \mid i = 0, 1, 2, \ldots\}$." Now, I'm new to ...
12
votes
2answers
232 views

Parsing arbitrary context-free grammars, mostly short snippets

I want to parse user-defined domain specific languages. These languages are typically close to mathematical notations (I am not parsing a natural language). Users define their DSL in a BNF notation, ...
10
votes
3answers
671 views

What are the possible sets of word lengths in a regular language?

Given a language $L$, define the length set of $L$ as the set of lengths of words in $L$: $$\mathrm{LS}(L) = \{|u| \mid u \in L \}$$ Which sets of integers can be the length set of a regular ...
6
votes
1answer
229 views

Can this CFG be written into an equivalent LL(1) grammar?

I have the following CFG which I suspect cannot be rewritten to one which is LL(1): $S \rightarrow \epsilon\ |\ aSbS\ |\ bSaS\ |\ cSdS\ |\ dScS$ I've thought about it for a while, and can't seem to ...
0
votes
0answers
34 views

$L = \{x\#x^R \mid x\in\{0,1\}^* \} $ not accepted by a queue automaton?

It can be proven that class of languages accepted by queue automata is equal to class of languages accepted by Turing machines. It was mentioned somewhere that the language $$L = \{x\#x^R \mid ...
0
votes
0answers
39 views

Union, Intersection, Difference, etc. of different types of languages

I am preparing for a competitive exam (GATE) in which questions are asked in Automata about operations among different types of languages. For example, If $L_1$ is recursive & $L_2$ is ...
1
vote
0answers
89 views

Is the complement of this language Context-Free $\{(a^nb^n)^m \mid n>0,m>0\}$?

I've been asked to decide whether a given language is a Context-Free Language (CFL). If yes, I should find the grammar that creates her, and if not, I need to prove it (with the pumping lemma). The ...
0
votes
2answers
39 views

what is the best way to approach the construction of nondeterministic PDA's?

I'm trying to construct a PDA for $L = \{w0^i1^j \mid w\text{ ends in } 01 \wedge 2i=3j\}$. My understanding is that I have to first accept an arbitrary number of zeros and ones and then ...
3
votes
2answers
96 views

Flowcharts vs DFA resp FSM equivalency

First I apologize if I confused therms DFA and FSM, to me it seems that is the same thing. The question is simple: Are the flowcharts (sequence, branching and jumping) equivalent to DFA resp. FSM? I ...
1
vote
1answer
36 views

Kleene star and Kleene plus

Let $\Sigma$ be an alphabet. Have a look at following definitions frequently used in literature containing Kleene star and Kleene plus. $\Sigma^* := \Sigma^+ \cup \{\varepsilon\}$ $\Sigma^+ := ...
0
votes
2answers
43 views

Kleene closure, concatenation problem

If $L_1 = \emptyset$ , $L_2= \{a\}$ then what is $$L_1\cdot L_2^* \cup L_1^*$$ The answer given is $\{\epsilon\}$ but I think it should be $\{\epsilon,a\}$. My Approach : $L_1^* = \{\epsilon\}$ ...
5
votes
2answers
86 views

Languages of cardinality higher than $\aleph_0$

I was studying model theory and that's how I came across formal languages. I looked around but it seems as though a language (set of strings over some alphabet) is usually treated as being finite or ...
0
votes
1answer
28 views

If $L$ is a $CFL$, then why isn't $L^*$ also $CFL$

I was studying closure properties of CFLs and I came across this. I want to understand why $L^*$ is not a CFL, can anyone explain me in depth with simple examples?
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votes
1answer
17 views

Language equivalence proof [duplicate]

Can anyone explain to me how the following is true for any language? $$L^+ = LL^* = L^*L$$ I'm confused because $L^*$ is the set of all words including the empty string, while $L^+$ is the set of ...
9
votes
1answer
563 views

Is there a context free, non-regular language $L$, for which $L^*$ is regular?

I know that there are non-regular languages, so that $L^*$ is regular, but all examples I can find are context-sensitive but not context free. In case there are none how do you prove it?
0
votes
1answer
33 views

Give an example of a non-regular language $L$ such that $L^*$ is regular [duplicate]

I can't think of an example of a non-regular language $L$ such that $L^*$ is regular. . Any help ?
2
votes
1answer
19 views

Can a language recognized by a NFA be recognized by a push down or Turing machine?

Every single NFA has an equivalent DFA representation so that every language recognized by NFA is recognized by the DFA, but is it also true that the language recognized by NFA is recognized by a push ...
2
votes
1answer
54 views

How to prove that the Myhill-Nerode equivalence classes for L are the same as for its complement?

Given language $L$, I want to show that its Myhill-Nerode equivalence classes are the same as for its complement $\overline{L}$. I am thinking of constructing a DFA $M$ for the Language $L$ so the ...
2
votes
0answers
41 views

Morse code is a ternary human-optimised code, is there a binary, non-machine optimised code? [closed]

Is Morse code without spaces uniquely decipherable? Discusses how Morse code isn't very clear without the third (usually) unseen element, the space. Is there a (historical?) human-optimised (vs. ...
1
vote
2answers
69 views

PDA recognising all strings with a $1$ in the second half

My professor gave us an old exam to look over for our final exam and I am having a hard time understanding the push down automata problem he gave. In the problem it says: Let $\Sigma = \{0,1\}$ ...
5
votes
2answers
2k views

Is 0* decidable?

I found a statement (without explanation) that a language $A = 0^*$ is decidable. How is that possible? I mean, how would we build a Turing machine that would accept (or reject) a possibly infinite ...
3
votes
2answers
73 views

Decide if this language is context free

I got this question for homework: Decide if this language is context free or not: $\qquad \{x@1^m: x \in \left\{0,1\right\}^*, m \in \mathbb{N}, x_m = 1\}$. Intuitively I think it's not ...