Questions about mathematical devices that read an input stream symbol by symbol and use a state transition map to produce an output stream, maybe using secondary storage.

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3
votes
0answers
32 views

context free grammar to NFA

I've been given an exercise to solve which goes as follows: generate an NFA from the given CFG, $$\begin{align*}S &\to AB \mid c\\ A &\to aAb \mid c\\ B &\to bBa \mid c\ . \end{align*}$$ ...
2
votes
1answer
45 views

NFA - string acceptance (decision problem) test

I am interested in testing for a given string (w) whether it is in the language (L) defined by a nondeterministic finite automaton (A). I have some blurry point in my mind. What is the complexity of ...
0
votes
1answer
35 views

Given family of grammars, determine if LR(k)

Parsing family of grammars, determine if LR(k) I have the exact same problem, but my reputation is not enough to comment on that thread, plus the OP hasn't been online in 2 years so I can't ask him ...
0
votes
0answers
38 views

Using A* to find the word closest to an input rejected by a finite automaton

In the article Fast approximate string matching with finite automata by M. Hulden (2009) (mostly pages 58/59), the author describes how to search for a closest matching string word from an automaton ...
3
votes
4answers
715 views

What is the point of finite automata?

Why learn finite automata when Turing machines do exactly the same thing? Turing machines accepts the same languages and more so what's the point?
2
votes
0answers
29 views

For $\sum = \{ 0,1 \}$, $A$ has strings which contain a $1$ in their middle third, and a $B$ which contain two $1$'s in their middle third [duplicate]

Language $A$ can also be represented as, $$A = \{ uvw \mid u,w \in \Sigma^*\text{ and, }v \in \Sigma^* 1 \Sigma^*\text{ and, }|u| = |w| \ge |v| \}$$ Language $B$ can also be represented as, $$B = \{ ...
2
votes
1answer
54 views

Help on using the pumping lemma?

I'm trying to prove that a language is not regular. That language is: {w ∈ {a, b}* | amount of a's in w is equivalent to the amount of b's in w, mod 2}. I have an inkling that this language is not ...
-2
votes
1answer
36 views

NFA: Regular Language that starts with ab but does not end with ab?

$L = \{x \in \{a,b\}^* \mid \text{$x$ starts with $ab$ but does not end with $ab$}\}$ I'm having trouble making a table for this NFA. I tried a few sketches out of the diagram and I can post them ...
1
vote
1answer
64 views

How to write a DFA where the second digit is equal to the last digit of binary strings?

I'm having some trouble writing a DFA for the language $$\{w =b_1\dots b_k \in\{0, 1\}^* \mid b \ge 2 \text{ and } b_2=b_k\}\,.$$ What I thought for this is writing a DFA where there are 4 states, ...
2
votes
3answers
90 views

Computing the closest match of an automaton and a string

I have a problem where I'm trying to find an efficient algorithm for approximate string matching for an input to the closest string match from an automaton (the input is assumed to be not accepting ...
0
votes
1answer
51 views

PDA - Sum of Two Characters = Sum of Two Other Characters

For one problem I have to solve, I'm given a Language: L = {a^r b^s c^t d^u | r+s = t+u} And from it told to construct a PDA that accepts it. I can construct a ...
-1
votes
1answer
39 views

Simple Pushdown Automaton

I'm currently learning about PDAs and their power when constructing them from Context-Free Grammars, however I'm still unsure of how to properly construct a CFG, and then a PDA from that CFG. In the ...
2
votes
0answers
17 views

Simulate NPDAs with DTMs using only polynomial overhead

We know by polynomial-time parsing algorithms like the classical CYK algorithm that $\mathrm{CFL} \subseteq \mathrm{P}$. Furthermore, it is easy to show by direct simulation that $\mathrm{DCFL} ...
0
votes
1answer
35 views

Can a DPDA be created for a Language which includes the null string?

Can a DPDA be created for a Language which includes the null string? The way I understand it, in a DPDA, you can have at most 1 move from any instantaneous description Delta(q,a,Z) where q is a ...
6
votes
3answers
857 views

How to XOR automata?

Say we have 3 DFAs. We know how to OR, AND, or NOT them. But how does one XOR them? There is not one single mention of this online. $x\; \mathrm{XOR} \;y\; \mathrm{XOR} \;z = ((x|y)(\neg x|y)|z) ...
3
votes
1answer
82 views

Efficient simulation of an NFA, while preserving the paths to the accept states

The standard way of simulating an NFA on a computer (for implementing regex engines etc) is to construct a DFA that accepts the same language. Otherwise you get problems like exponential blowup. ...
0
votes
0answers
16 views

DFA transtion table [duplicate]

I have the following DFA transition table for the regular expression ab. I don't understand these hyphens.As we know DFA is a deterministic automata and each state is defined for both a and b. ...
-3
votes
1answer
45 views

Creating a DFA that only accepts number of a's that are multiples of 3

I am brand new to DFA's and my first exercise requires me to create a DFA instance such that the number of a's in the string is a multiple of 3. We only have two types of symbols: a, b. To my ...
0
votes
2answers
50 views

What does an NFA do if there's no transition with the correct symbol?

So I am learning about DFA and NFA, and I need some clarification for it. DFA accept empty set transition for every element in the alphabet path are deterministic NFA accept the empty set ...
-1
votes
1answer
50 views

Converting DFA to regular expression [duplicate]

I have the following DFA. (Yellow stated are accepting states.) I want to eliminate states step by step to find the regular expression of it. In my steps, I think there is a bug because I do not know ...
0
votes
1answer
49 views

How to prove that $\{0^n 1^{5n} \mid n \ge 10000 \}$ is not a regular language?

I proved that $$ \{ 0^n 1^{5n} \mid n \geq 0 \}$$ is not a regular language using Pumping Lemma by following way. Solve by contradiction that $ L = \{0^n 1^{5n} \mid n \geq 0 \}$ is regular ...
1
vote
2answers
47 views

What is the purpose of ϵ-transitions in PDA?

$A = \{a^i b^j c^k\mid i = j\text{ or } j = k; i, j, k \ge 0\}$. In its push down automaton should not there be the red colored transition instead of the black colored one?
0
votes
1answer
53 views

LR(0) expressive power

So I have grouped the following formalisms into a power hierarchy (and made classes for them): Class 1 DFA NFA NFAϵ reg.exp Class 2 (DCFL expressivity?) LR(1) DPDA Class 3 CFG PDA Class 4 ...
0
votes
1answer
60 views

Intersections of some context-free languages

Suppose We have Some language as follows: $L_1=\{w^* | w=x \text{ and } x \in \Sigma^*\}$ $L_2=\{ww^R ww^R | w \in ( \Sigma + \Sigma)^*\}$ $L_3=\{w | w=xy, x,y \in \Sigma^*, y \text{ is a ...
-1
votes
1answer
40 views

Equivalence of some Automata & Language & NFA

I read some note about Automaton Course. i see this note, that following all is the same. but i think the L(g) is not equal to NFA and regular expression. anyone could help me with defining the ...
0
votes
1answer
57 views

Set containment of MinimumBadPrefix and BadPrefix of a Safety Property

This question is related to formal model checking theory, but I cannot find a tag for it. Let $P_{safe}$ be a safety property. $BadPref(P_{safe})$ is the set of bad prefixes for $P_{safe}$ A Safety ...
-1
votes
1answer
95 views

How to determine the set of numbers read by a DFA from one state to another?

Using the Deterministic Finite Automaton (Q, Σ, Δ, q_0, F): Alphabet: Σ is {(0 0), (0 1), (1 0), (1 1)} Definition of Δ to strings recursively: Δ*(q, ε) = q for all q ∈ Q Δ*(q, xa) = Δ(Δ*(q, x), ...
0
votes
1answer
70 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..?
2
votes
1answer
39 views

Using induction to prove transition states are the same

Suppose that you have a DFA $M=\left(S,\Sigma,s_0,\delta,{s_f}\right)$ with $s_f\neq s_0$. Suppose further that, for all $a\in\Sigma$, $\delta\left(s_0,a\right)=\delta\left(s_f,a\right)$. Show that ...
0
votes
0answers
17 views

Classification of one-dimensional CA based on the number of inputs each cell receives during an update?

Consider Wolfram's rule 30 and Wolfram's rule 62. In the case of rule 30, only two bits of information must be passed to each new cell in the CA during an update, while for Wolfram's rule 62, three ...
0
votes
1answer
49 views

Is a door lock a finite state machine?

Must the states of a finite state machine be worked off sequentially or could you understand the different shaped parts of the key as input and the position of the pins as states? If not all the input ...
1
vote
1answer
26 views

Why does a DFA either contain all or no words $a^k$ if it loops for $a$ in all states?

I am trying to solve this particular problem from Automata Theory by Ullman, Hopcroft, it is as shown below: Let $A$ be a $DFA$ and $a$ be a particular input symbol of $A$, such that for all ...
2
votes
1answer
75 views

Computational equivalences between a calculus and an automaton model

This Wikipedia table (template for "Formal languages and grammars") maps grammar to language to abstract machine for more than a dozen languages. ...
0
votes
1answer
37 views

NFA state complexity for the complement of EPAL restricted to a fixed length

I've been having trouble proving the next statement: Let $L_n=\{ww, |w|=n\}$ (the set of equal-length palindromes (EPAL) restricted to length $2n$). Prove that $L^c_n$ can be accepted by an NFA ...
-1
votes
1answer
102 views

Converting NFA to regular expression

Here is the regular expression I made for it This is my first answer, used the naive method aka don't know what am doin' method. $$ \epsilon \cup a^* \cup (a^*b) \left((a| b^*a) | \left( ...
1
vote
1answer
68 views

Don't understand closure under string reversal

I am trying to learn from http://www.cs.uiuc.edu/class/su08/cs273/lectures/lect_06.pdf #2 and I understand everything except for the 2nd line of delta prime prime function, I having breaking down ...
1
vote
0answers
71 views

Given a non-deterministic Mealy machine $M$, if $L$ is regular, is $M(L)$ regular?

Consider a nondeterministic Mealy machine, $M$, defined as follows: $M = (Q, \Sigma, \Delta, \delta, \tau, q_0)$ where $Q$ is a finite set of states $\Sigma$ is an input alphabet $\Delta$ is an ...
1
vote
0answers
27 views

Describe in English the pattern in the following regular expressions [duplicate]

Describe (in English phrases) the languages associated with the following regular expression. it says to be as simple as possible ...
1
vote
1answer
29 views

Sampling from a Acyclic Deterministic Finite Automaton

Assume you have a finite language $L$ succinctly represented as a acyclic DFA $M$ (models can't be much simpler than that :) ). How can we efficiently sample a word from $L$ with uniform ...
-3
votes
1answer
124 views

Pushdown Automata Challenge

I read one old-midterm exam on Automata. consider: the language that accepted by above pushdown automata is not generated by which of the following grammar? 1) S->aBaa|a$\epsilon$ ...
-1
votes
1answer
34 views

Do NFAs with ϵ-transitions accept languages that no PDA can?

Is it correct to say that there are languages that a NFA with epsilon recognizes but a PDA is not? I think that it is wrong but I cannot find a suitable explanation.
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votes
2answers
60 views

Strange TM Language on Definition [closed]

i prepare for Autotmata Course Final Exam. in one of lecture, our professor draw this Turing Machine, and wrote DELTA is Neutral element of TM. it'w wrote: Language of this TM is: {$W \in ...
1
vote
1answer
208 views

Deciding if a finite automata accepts strings of any length

Question is you're given a DFA. Give an algorithm which tells you whether strings of all lengths $n\in \mathbb{N}$ are acceptable or not. What I doing was, I have algorithm to count the number of all ...
3
votes
1answer
47 views

Converting generalized NFAs to NFAs

I came across generalized nondeterministic finite automata (GNFAs) in Sipser's Introduction to the Theory of Computation. These are automata where transitions are labelled with regular expressions, ...
-1
votes
1answer
111 views

How to construct a DFA for this?

Let $C = shuffle(A, B)$ denote the shuffle $C$ of two languages $A$ and $B$, it consists of all strings $w$ of the form $w = a_1b_1a_2b_2....a_kb_k$, for $k > 0$, with $a_1a_2 ··· a_k \in A$ and ...
-1
votes
1answer
53 views

Why is there still nondeterminism in my automaton?

I've been solving some exercises recently and it appears my answer was wrong for this particular example. The task is to convert this NFA into a DFA: My attempt is this: Now the tool I'm using ...
-2
votes
1answer
159 views

Why is the language of even-length non-palindromes context-free?

We know $L_1=\{w_1 w_2 \in (a+b)^*\mid |w_1|=|w_2|, w_2 \neq w_1^{\;\mathrm{R}}\}$ is a context-free language. Can anyone help me produce a PDA or give me any hint how I can quickly understand why ...
-3
votes
1answer
64 views

Language of a grammar

What's the language of following grammar? $G: S \to S_1B$ $S_1 \to aS_1b$ $bB \to bbbB$ $aS_1b \to aa$ $B \to \lambda$ any hint or solution?
0
votes
0answers
20 views

Converting DFA to Regular Expression “equation-method(?)” [duplicate]

I have trouble understanding my text-book on how to convert a DFA to a Regular Expression using "equation-method"(don't no what it's called). If someone could explain step by step in detail what's ...
1
vote
1answer
91 views

Non Deterministic PDA accepted language not clear

This is a PDA from the lecture slides I'm using: They say it accepts all words that contain double a's. While it makes some sense it's not full proof. What prevents the second a to be read in the ...