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

learn more… | top users | synonyms

1
vote
1answer
16 views

is language accepted by finte state automaton

Hi I need to prove these languages are accepted or not by the following finite state automata. for 1 does this mean that we need an even number of a's or that a is literally 2,4,6,8....etc also ...
0
votes
2answers
36 views

Is this language Regular or is it not?

$L=\{0,011,011000,0110001111,\dots \}$ Generates string of the form: $0^1 \\ 0^1 1^2 \\ 0^1 1^2 0^3 \\ 0^1 1^2 0^3 1^4 \\ 0^1 1^2 0^3 1^4 0^5\\ \dots$
2
votes
1answer
36 views

Why is this language not regular?

I am studying Automata using the Coursera course created by Jeff Ullman. On slide 36 of this presentation: http://spark-public.s3.amazonaws.com/automata/slides/3_fa2.pdf it says that the language is ...
4
votes
3answers
131 views

Number of states in a finite automaton

How many states are required by a deterministic finite automaton to store $m$ words each of length $n$? I came across $2^{mn}$ as the solution but there was no explanation.
1
vote
1answer
22 views

How to simulate a 3-stack automaton with a 2-stack automaton?

Since a 2-stack automaton is Turing-equivalent, it is possible to simulate a 3-stack automaton with just a 2-stack automaton. But how so? How it is normally done?
0
votes
1answer
442 views

Create DFA that accept language where number of 0's is even and after every 1 goes 0

Alphabet ${} = \{0,1\}$. Language $L = \{ w \in \{0,1\}^* \mid \text{ number of $0$'s in $w$ is even and after every $1$ goes $0$} \}$. I'm trying to create DFA that accepts language $L$. ...
2
votes
1answer
38 views

Is the Champernowne constant an automatic number?

The Champernowne constant in base $b \geq 2$ is obtained by concatenating the $b$-ary expansion of every integer. For example, in base $10$ this is $$ 0.123456789101112131415\dotsc $$ Question: Is the ...
1
vote
1answer
20 views

Why Petri Net tokens are not added?

Reading this article it says: A firing of an enabled transition removes one token from each input place and adds one token to each output place. Now if I have the following net, with all ...
0
votes
0answers
9 views

inverse proof of closed under union

I am being posed the following question: given are languages $L_1, L_2, L_3 $ and $ L_4$. $L_1$ is a decidable language and $L_2$ and $L_4$ are both recognizable languages. Considering $L_1 = L_2 ...
16
votes
3answers
22k views

Difference between NFA and DFA

In very simple terms please, all resources I'm finding are talking about tuples and stuff and I just need a simple explanation that I can remember easily because I keep getting them mixed up.
1
vote
1answer
42 views

How n (1+b) is not prime?

Here is the complete proof taken from this link How do I convince myself that n(1+b) is not prime when b>=1? Here is what I did: if n is 3 and b is 3. Then ...
2
votes
1answer
613 views

Finite state machine

I am doing discrete math, and we are studying Finite State Machines. But i am a little confuse on how to do this. Here is a question, Write a regular expression for the language, and define a finite ...
0
votes
2answers
26 views

Why is the below language regular?

If I have a language $$L=\left\{wxwy : w,x,y \in \{a,b\}^+ \right\}$$ I am not getting how come we are able to write regular expression for this of the form $$a(a+b)^+ a(a+b) ^+ + b(a+b)^+ b(a+b) ...
1
vote
2answers
41 views

Proving that $L := \{a^n\mid\exists k \geq 0\ n = k^3\}$ is not a regular language

I'm having trouble using the pumping lemma to prove this language $L := \{a^n\mid\exists k \geq 0\ n = k^3\}$ is not regular. Assume $L$ is regular. Thus there is a DFA $M$ for it. Choose $m$ as the ...
0
votes
1answer
31 views

Quick question on DFA

I'm asked to list all DFA over the alphabet sigma = {0} such that the set of states is {s0, s1}, for which the initial state is s0 and the set of accept states is either {s0} or {s1}. And also asked ...
2
votes
1answer
29 views

pumping lemma for CFL vs pumping lemma for regular languages

Is the pumping lemma for context free languages a generalization of the pumping lemma for regular languages (for instance if we set $u=\epsilon, v=\epsilon$ we can then relate $wx$ in the pumping ...
3
votes
1answer
792 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 ...
0
votes
0answers
19 views

Best approach to determine the equivalence classes of a formal language

I created a minimum automaton for a formal language using the Myhill-Nerode theorem. The language for which I created the automaton is defined by $L=\{w \in \{a,b\}^*:w=av \text{ for a word } v ...
1
vote
0answers
29 views

Construct PDA that accepts the language $ L = \{ w \in \{ a,b,c\}^*; |w|_c=|w|_a + |w|_b \} $

Problem Construct PDA that accepts the language $ L = \{ w \in \{ a,b,c\}^*; |w|_c=|w|_a + |w|_b \} $ My first idea was this: There can be an "a","b" or a "c" at the beginning of a word Then we ...
0
votes
2answers
23 views

How to draw a DFA for complement of a regular language using a regular expression?

How can I draw an FA for the complement of the language $L(r)$? $L(r) = a^* (aba^*)^* b^* a^*$ I can draw an FA for $L(r)$ and convert to DFA and then take the complement, however it seems very long ...
3
votes
1answer
96 views

Determine the language that corresponds to the following automata.

I want to determine that language that corresponds to the following automata Note: $q_{6}$ have arrow to $a$ to himself. I started with the minimal words: $aaabb$ $aaba$ $aaaba$ $bababa$ the ...
2
votes
1answer
18 views

Concatenation of Finite Languages and Regular Languages

I know that the following statements regarding Concatenation are false. However, I'm having difficulty explaining why they are false with simple counter-examples. I'm able to find simple ...
0
votes
1answer
33 views

Context-free language or not

It is language: $L = \left\lbrace a^ib^jc^kd^l \mid i+k < j+l+3 \right\rbrace$ Is it context-free or not? I have two versions: 1)Pumping lemma(refute): get a word $uvxyz = aabcd$ if $i=2$ we get ...
1
vote
1answer
62 views

Why are Recursively enumerable languages closed under intersection?

when Recursively enumerable sets are not closed under complement ,then how come they are closed under intersection because the definition of intersection comes as L1 intersection L2= complement(L1' ...
-1
votes
2answers
25 views

Is the intersection of a finite language and an infinite language always a regular language?

Is the intersection of a finite language $L_1$ and an infinite language $L_2$ always a regular language? I've tried a few examples and the result always seems regular. $\{\} \cap a^nb^n = \{\}$ ...
1
vote
2answers
729 views

Find a CFG for L = { a^nb^m : n != m }

This question is upcoming for my midterm and I can't figure it out. My professor broke it down in two statements (n>m) and(m>n) and left us at that. Find a context free grammar for $L = \{ a^n b^m : ...
2
votes
1answer
18 views

Finding regular expressions for which a given Turing machine halts and accepts, halts and rejects, and diverges.

Consider the Turing machine M = (Q,Σ,Γ,δ,q,F) F = {t} Q = {q,r,s,t,v,x} Σ = {a,b,c} Γ = {B,a,b,c} δ = [q,a,q,a,R] [q,b,q,b,R] [q,c,v,b,R] [q,B,r,B,L] [r,a,s,B,L] [r,b,s,B,L] [r,c,s,B,L] ...
0
votes
1answer
49 views

Context free grammar $\{a^n b^m c^k\; : \;k>m \; \; k>n\}$

Is this a CFL? $$\{a^n b^m c^k\; : \;k>m \; \; k>n\}$$ When on seeing $a$'s and $b$'s I push them onto stack and as I see $ c$ as input if $ TOS$ is $b$ ,I pop them ,again if $TOS$ is a,I pop ...
0
votes
1answer
18 views

Proving from Myhill-Nerode that the minimum DFA is the smallest automaton recognizing $L$

From this paper, In the proof of (Myhill-Nerode theorem) it's stated that if $L$ is a regular language and the index of $\sim_L$ is $i_L \in \mathbb{N}$ then it's both necessary and sufficient for ...
1
vote
1answer
26 views

Minimum Size of DFA

I'm confused about the following DFA problem: Let L denote the set of all strings in $\{a, b\}^∗$ that contain abb or aab as a substring. Show that any DFA that decides L must have at least five ...
1
vote
1answer
33 views

Construct a deterministic finite state automaton

Construct a deterministic finite-state automaton that recognizes the set of all bit strings that end with 10. This is what I drew. Not sure if its correct. State 2 is the final state. Am I missing ...
0
votes
1answer
20 views
0
votes
0answers
13 views

4th case in Ogden's Lemma

I'm trying to understand Ogden's Lemma and I know there are four cases, but in the next example I can only find 3: A = {$0^n1^m0^k$ | k = max{n,m}} is not context free: Assuming: z = $0^k1^k0^k ∈ A$ ...
0
votes
1answer
23 views

How to find the right quotient of a language given two languages?

If $L_1= \{a^n b^m \mid n \geqslant 1, m \geqslant 1 \} \cup \{ba\}$ and $L_2= \{b^m \mid m \geqslant 0 \}$. I am not getting how the DFA for $L_1/L_2$ is constructed in the second figure ...
2
votes
1answer
43 views

Designing a Turing Machine - low level transitions

I couldn't figure out how to proceed with this question. Preparing for the finals, can someone explain how to do this step by step? Design a TM, write low level transitions for $\{a^i b^j :i ≤ j ≤ ...
0
votes
1answer
29 views

Graph and language/automaton equivalence

I'm looking for a reference rather than an answer. I think I'm just not Googling the right combination of terms. I imagine that there is a class of graphs which is equivalent to some class of ...
1
vote
1answer
29 views

Let $LOOP_{TM}$ be descriptor language of all touring machines that won't halt for any input. Show reduction of $HALT_{TM}$ to $LOOP_{TM}$

Question from Homework that I'm having difficult to answer on: Let $LOOP_{TM} = \{\langle M\rangle \mid \text{M is a TM that does not halt on any input w}\}$ Let $LOOP_{TM}$ be descriptor ...
0
votes
2answers
31 views

Converting an NFA to DFA

I am atttempting to convert an NFA into an equivalent DFA. I did it, but i am not sure if it is correct. If anyone can please take a look at let me know if it is correct or if there is something wrong ...
4
votes
2answers
3k views

Finite automaton that recognizes the empty language $\emptyset$

Since the language $L = \emptyset$ is regular, there must be a finite automaton that recognizes it. However, I'm not exactly sure how one would be constructed. I feel like the answer is trivial. ...
0
votes
2answers
15 views

Languages and their Regular Expressions - Automata

I am working on some Automata practice problems. I am working a 2 part question. Here it is: Let $\Sigma = \{a,b\}$ be an alphabet. Let $L = \left\{w \in \Sigma^* \mid n_a(w) \le 4\right\}$ ...
1
vote
1answer
25 views

Pumping Lemma proof and the union/intersection of regular and non-regular languages

I am still learning the pumping lemma. I have a problem for which I used it. I used it on the first part (a) but I am unsure if it is correct. Parts b-d, I am not sure how to do it. I created a dfa ...
0
votes
1answer
20 views

Using the Pumping Lemma To Prove A Language Is Not Regular

I am taking a Automata class and we just went over the Pumping Lemma. Initially, it did not make sense. I am still not fully comfortable but I have started trying to use it to prove that a language is ...
2
votes
2answers
43 views

A Regular Expression for all strings that…

I got a problem I have to solve, the problem says that given an alphabet $\Sigma = \{a, b, c\}$ I have to build a regular expression that describes the string with: An even number of a's. A 4k + 1 ...
2
votes
1answer
19 views

Prove that regular languages are closed under operation

Operation $random$ is defined on two words with equal length in the following way: $\forall w_1,w_2 \in \Sigma^* s.t. |w_1|=|w_2|=n, w_1=a_1a_2...a_n, w_2=b_1b_2...b_n:$ $Random(w_1,w_2) = ...
1
vote
1answer
66 views

Difference between a*b and a*+b? Does the “+” denote Kleene plus or “or”?

Me and a friend are study for a quiz and are trying to determine the difference between the two NFA's produce by the regular exressions a*b and ...
0
votes
1answer
26 views

Explain the semantics of concurrent languages with real analysis examples

In computer science, concurrency is a property of systems in which several computations are executing simultaneously, and potentially interacting with each other. I need to explain the concurrency ...
0
votes
1answer
56 views

How to prove the language of all binary numbers that are prime is nonregular using pumping lemma?

How to prove the language of all binary numbers that are prime is not regular using pumping lemma? I have seen Can an infinite set of primes be a regular language or CFG? We have not studied the ...
5
votes
2answers
3k views

How to show that $ALL_{DFA}$ is in P

How can I show that $ALL_{DFA}$ is in P ? $ALL_{DFA} = \{ \langle A \rangle \mid A \text{ is a DFA and } L(A) = \Sigma^* \}$
0
votes
0answers
86 views

Determinitic finite automaton (DFA) that accepts natural numbers divisible by 6

I'm new to Formal Systems and Automata and I'm working on some exercises to get familiar with the concepts. I want to create a DFA that accepts natural numbers divisible by 6. I know that a number ...
1
vote
1answer
45 views

NFA (nondeterministic finite automaton) made out of the Bible?

Let B be the language over alphabet {a, ... z} consisting of those words occuring in the Bible. Thus, B = {in,the,beginning,god,created,...}. Describe an NFA whose language is B. Describe what ...