Automata Theory, including abstract machines, grammars, parsing, grammatical inference, transducers, and finite-state techniques

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2
votes
1answer
37 views

Show that the function floor-log is primitive recursive

I have been stuck on this problem for a while and I was hoping someone could help me with it. This is for my computer science automata and formal languages class. Given an integer $b$ greater than or ...
0
votes
1answer
36 views

Push Down Automata

I've been stuck on this one problem for a couple of days now with no clue on how to complete it. Construct a PDA which accepts precisely the language $\{a^{2n} (bc)^n\mid n \in \mathbb{N}\}$. ...
0
votes
1answer
43 views

Proving an operation is closed under regular languages

Following operation is defined over languages where $n \in \mathbb{N} :$ $L \ominus n = \lbrace s \in \sum^* | \exists s^{'} \in \sum^* (length(s^{'})=n,ss^{'} \in L) \rbrace$ Meaning that $L ...
0
votes
0answers
27 views

How to prove that Pumping lemma can't be used to prove regular languages.

I need a prove that pumping lemma can't be used to prove regular language. Pumping lemma is only used for proving non-regular language, but I need to show that how it can't be used to prove regular ...
-1
votes
2answers
31 views

How to Solve Complex Non-Regular Language? [closed]

$L_5={\{ c^n a^m b^p,n+m=p,p≥6}\}$ where $∑=(a,b,c)$ I need little help, I was practicing Pumping lemma, and I encountered this language, I saw these conditions and I got totally confused, what to do ...
0
votes
1answer
19 views

Are these languages Regular or Non-regular?

I have these two languages $L={\{a^n b^m,n≥m+5,m>0}\}$ Where $∑=(a,b)$ $L={\{a^n b^m,n≥m+5,m≤5}\}$ Where $∑=(a,b)$ As you can see that there is only one difference, the condition of ...
1
vote
2answers
44 views

Why |w|>=m in pumping lemma?

If L is a regular language, then there exists a constant n (which depends on L) such that ...
0
votes
1answer
22 views

Why does this concatenation doesn't work for these 2 dfa's [closed]

I have the following deterministic finite automaton which accepts an even number of 0's. and this automaton which accepts an odd number of 1's: I want to concatenate these 2 automatons. I ...
1
vote
1answer
24 views

Two DFA to one NFA.

Let assume that I have given DFA $D$ which recognize language $L$. Now I would like create the DFA/NFA which recognize the language $L'$. $$ L' = \{ w \in L : |w| = 2k, k \ge 0 \}$$ In words, $L'$ ...
0
votes
0answers
27 views

Theory automata. Proof. [duplicate]

Let $A/B= \{ w : wx \in A \}$ for some $x \in B $. Show that if $A$ is regular and $B$ is any language, then $A/B$ is regular. Please hint me with doing it using Myhill-Nerod's theorem. I observed ...
-1
votes
2answers
25 views

Decomposing an infinite regular language

Let $L$ be an infinite regular language. Prove that $L$ can be split up into $L_1, L_2$, so that $L_1 \cup L_2 = L$ and $L_1 \cap L_2 = \emptyset$ Can you give me some directions to do it? Thanks ...
0
votes
1answer
41 views

Convert the regular expression to a NFA

I have to convert the following regular expressions to a NFA: $$(0 \cup 1)^{\star} 000 (0 \cup 1)^{\star}$$ $$(((00)^{\star} (11)) \cup 01)^{\star}$$ $$\emptyset^{\star}$$ $$a(abb)^{\star} \cup ...
1
vote
1answer
37 views

Write the regular expression of the language that the DFA accepts.

I am given a DFA and I have tried to write the regular expression of the language that it accepts. This is the DFA that I am given: I have found some words that the DFA accepts: ...
1
vote
2answers
43 views

Convert NFA to DFA

I have to convert the following NFA's into the equivalent DFA's. I have done the following: Could you tell me if it is correct??
0
votes
2answers
34 views

Finding the regular expression

I have the problem below: I need to find the regular expression of the set of strings where $n(a)+n(b)$ is an even number (where $n(a)$ is the number of $a$'s and $n(b)$ is the number of $b$'s) .. I ...
-1
votes
1answer
26 views

Automata accepting

Let $A = \{ a,b\} $ and $ L = \{ w \in A^* : |a| = 2k+1, |b| = 2l, k,l \ge 0 \}$ $|a| = 2k+1 $ means that amount of 'a' in word $w$ should be odd. I am asking for any advice. I tried do it a lot of ...
1
vote
1answer
45 views

Regular expressions

I have this assignment and I have to prove that $$ (b+aa^* b)+(b+aa^* b)(a+ba^* b)^* (a+ba^* b) = a^* b(a+ba^* a)b^* $$ How do I prove this? What I have is this: $$\begin{align} \text{LHS} ...
-1
votes
1answer
35 views

Show that every recursively enumerable set is accepted by a Turing machine with only two non accepting states and one accepting state.

A recursively enumerable set is a set where you can write a program that will output each element in the set: E1, E2, E3... it's okay if this program never stops. For more info look here : ...
0
votes
1answer
32 views

Closure of regular languages, Star Operator

Show with a counterexample that the following construction doesn't prove the closure of regular languages at the concatenation. In other words, find a NFA $N_1$ such that the NFA $N$ of the ...
0
votes
1answer
29 views

the minimal deterministic finite automaton recognizing $\{1^n 0^n /n\leq N\}$

Given a language $L$ how can I determine the number of states of the minimal automate which recognizes $L$. I want some examples and to understand the methods that we can use to find a lower bound for ...
0
votes
1answer
59 views

Prove that $A/B$ is regular when $A$ is regular and $B$ is regular or not regular.

Prove that $A/B$ is regular when $A$ is regular and $B$ is regular or not regular. $$A/B=\{w: wx\in A\ \text { for some }\ x\in B\}$$ Please give me a clue.
2
votes
0answers
38 views

show that language is regular

Let $B_n = \{a^k\ |\text{ where } k\text{ is a multiple of } n\}$. Show that for each $n\ge 1$ the $B_n$ language is regular. My proposition of solution: What about it ?
1
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3answers
50 views

Show that a language is regular

Show that language $B$ is regular: $$B = \left\{1^ky\mid y\in \{0,1\}^*\right\} $$ $y$ contains $\ge k$ symbols $1$ So I try in following way - I'll draw DFA: What about my solution? Is it good?
0
votes
0answers
43 views

Intersection of 2 deterministic finite state automata, but nondeterministically

Starting from 2 simple deterministic finite state automata, I need to construct a non-deterministic automaton that accepts the intersection of the two inputs. Using the algorithm presented at ...
1
vote
2answers
56 views

What the way studying math to automata theory

Good day everyone. I need to know automata theory. Can you advice me the best way to study math? What themes will I need to know to understand automata theory. What a sequence of study? What level ...
3
votes
0answers
99 views

Converting a pushdown automaton (that accepts by final state) to a context-free grammar

Given the following PDA: $$ P = (\{q, p\}, \{0, 1\}, \{Z_0, X\}, \delta, q, Z_0, \{p\}) $$ where the transition function $\delta$ is given by: $$ \delta(q, 0, Z_0) = \{(q, XZ_0)\} \\ \delta(q, 0, ...
1
vote
1answer
36 views

Is the empty set/language contained in the following set

Assume I have the following set of languages: $$ \{L \subseteq \{0,1\}^* \mid \text{for all $w \in L$, $|w| \leqslant 3$}\} $$ I know it contains the language containing the empty word since the ...
0
votes
0answers
109 views

Automata to detect numbers divisible by $7$

I have a task and I really have no idea how to solve it. Build deterministic finite automata such that it can detect numbers divisible by $7$. So our alphabet is $\left\{0,1,2,3,4,5,6,7,8,9\right\}$ ...
1
vote
1answer
33 views

Show that the language is regular - Closure

For languages $A$ and $B$, let the perfect shuffle of $A$ and $B$ be the language $$L=\{w \ \mid \ w=a_1 b_1 \dots a_k b_k, \text{ where } a_1 \cdots a_k \in A \text{ and } b_1 \cdots b_k \in B, ...
0
votes
1answer
32 views

Show that the language is regular

Let $$B_n=\{a^k \ \mid \ k \text{ is a multiple of } n\}$$ Show that for each $n \geq 1$, the language $B_n$ is regular. $$$$ Could you give me some hints how we coukd show this?? Do we have ...
0
votes
1answer
30 views

Construct the DFA of the language

I have to construct a DFA for the language $$\{w \mid w \text{ has exactly two } a's \text{ and at leat two } b's\}$$ To construct it we have to construct first the DFA's for the languages $$\{ w ...
0
votes
2answers
50 views

Checking Understanding of DFA Regular Operations - Intersection and Star

I'm currently taking a Logics course, and trying to understand the regular operations, intersection and star. I have a question regarding the work I have done so far. Given the following ...
-1
votes
1answer
53 views

$L_{a}= \{w_{1}cw_{2} : w_{1},w_{2} \in \{a,b\}^{\ast}, w_{1} = w_{2}\}$ [closed]

Why the following is not context free? Anyone could describe it for me. $L_{a}= \{w_{1}cw_{2} : w_{1},w_{2} \in \{a,b\}^{\ast}, w_{1} = w_{2}\}$
0
votes
1answer
23 views

Reference for finite state automaton

I am studying Grigorchuk's groups and it involves somewhat theory from Finite state automatons which I have never had any encounter before. Can somebody suggest me what are the best but self readable ...
2
votes
3answers
22 views

Name for a state of an automaton that can't be left

In an automaton, we might have a state that once reached cannot be left. It is for example for Ø in Is there a common/official name for such a state ?
0
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0answers
28 views

Design a Two-Tape Turing Machine which generate Palindrome

For e.g I have a String on a tape, $Blank|1|0|1|0|Blank$. Now I have to Use two tape and Reverse this string into second tape. First tape =$Blank|1|0|1|0|Blank$. ...
0
votes
0answers
25 views

Design a Turing machine to check whether an input is prime or not. [duplicate]

This is an assignment, I need to make a primality checking turing machine, which check whether an input is prime or not. what i've done so far is that i made this logic which is, ...
2
votes
1answer
198 views

Construct a Turing-Machine for Factorial(unary)

I am designing a turing machine which calculates the factorial of any given input for example, $3! = 3.2.1$, on tape it will look like this $Blank|1|1|1|Blank$ What I have done so far is that, I made ...
4
votes
0answers
114 views

Designing a turing machine for primality check.

I am designing some turing machines, so far I have made Binary Addition and subtraction. Now I've been thinking that what if turing machine can check if the number is prime or not. Lets suppose we ...
0
votes
1answer
15 views

NFA from regular grammars

I am trying to make an NFA from this regular grammar $$\{a^n \mid n > 0\}\cup \{b^m a^k \mid m\ge 0,k \ge 0\}\;.$$ This is what I have now. The last part, $a\ge 0$, is the one I am not sure ...
0
votes
1answer
25 views

Attractors of a Random Boolean Network?

I need some direction on the topic of Random boolean networks (NK-boolean networks or Kauffman automata). I now some of the results like if K=1 the systems settles down to fixed points, if K=2 it ...
0
votes
1answer
45 views

DFA automaton that recognizes the following language

Need to construct a DFA automation that recognizes the following language of strings over the alphabet {a,b}: The set of all strings that contain the pattern baa and end with b. (So, for example, your ...
2
votes
1answer
590 views

Designing a Turing machine for Binary Multiplication

I need help designing a turing machine that will compute the following $$f(x,y) = x\times y$$ How to approach this problem in binary base? This is a assignment so I don't want anyone to solve it ...
6
votes
4answers
72 views

Can this set of rules perform all Boolean operations?

I never worked in this field before, I just thought about this set of rules and never saw something similar before. I apologise if I don't use the right mathematical vocabulary for my question. ...
0
votes
1answer
109 views

Context Free Grammar and some details [closed]

Why this grammar shows a Context Free and Linear Language, (i.e, not context sensitive or non-context free). S -> SBA | a BA -> AB aA -> aaB B -> b
1
vote
2answers
32 views

Algorith/ Equation to get the ith element in N x N

I am having a difficulty figuring out the equation to get the ith element in $\mathbb{N}\times \mathbb{N}$ ( crossing the set of natural numbers).We have $\mathbb{N}\times \mathbb{N} = \{ ...
0
votes
1answer
38 views

Prove the following context-free language is generated by this grammar.

I would like to prove the context-free language $$ \mathcal{A} = \{ w\#x ~:~ w^R \text{ is a substring of $x$ for } w,x \in \{0,1\}^* \}, $$ has the context free grammar \begin{align*} ...
1
vote
1answer
22 views

Language described by inverting accepting states of NFA

What is the formal language described by inverting accepting states of NFA? By inverting, I mean that rejecting states become accepting states and accepting states become rejecting states. Is there a ...
3
votes
2answers
63 views

Is the language “substrings of an even-lengthed regular language” also regular?

I want to prove that for a regular language $L$ where $\forall w \in L$ the length of $w$ is even, the language containing the first halves of the words of $L$ and the language containing the second ...
1
vote
2answers
37 views

NFA construction problem

I need to construct an automaton that recognizes the following language of strings over the alphabet $\{a,b\}$: The set of all strings over alphabet $\{a,b\}$ with the subsequence $abba$. (A ...