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

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Properties of a valid DFA

Is a DFA required to have transitions on each input symbol from each state defined? If there isn't a path from state q1 to another state on input a for example, does that invalidate the DFA itself. ...
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308 views

Is it always possible to convert a non-deterministic PDA to a deterministic one?

Is it always possible to convert a non-deterministic PDA to a deterministic one? What is the significance of this observation for the computing power of contex-free grammars?
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What is the difference between regex operations in math and regex in UNIX / Linux?

What is the difference between regular expression operations (union, concatenation, kleene star) and regular expression (implemented in UNIX and can be used together with the grep command)? Are there ...
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Determine whether $L=\{w:|w|_a=2^n+273\text{ for }n\in \mathbb{N}\}$ is regular.

Given the alphabet $\Sigma=\{a, b\}$ and for the next Language $L=\{w:|w|_a=2^n+273\text{ for }n\in \mathbb{N}\}$ determine whether the language is regular. Firstly, I think this language is regular. ...
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Subset of A Regular Language

I need to show that a subset of a regular language is regular or not. I think it may not be regular but I could not find a counter example. Do you have any simple example to prove that? Thanks in ...
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260 views

An infinite context free language can be split into two infinite regular languages

Prove or disprove Let $L$ be an infinite context free language. Show that there exists a regular language $R$ such that $ L \cap R $ and $L \cap \overline{R} $ are infinite and regular.
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Number of states required for deterministic finite automata

Lemma in text: Let $c$ be a constant and $L = \{1^c\}$ (the singleton language containing the string of $c$ many 1's). Then no DFA with < $c$ states can accept $L$. The given proof assumes ...
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Confusion related to a property of languages on some alphabet V

I came across this relation betwen tww sets of languages formed from the alphabet V. A,B The relation is $$ A^*\cup B^* =((A\cup B)^*)^* $$ I am confused how this is derived. Any pointer?
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Deterministic finite automata [closed]

For this question about Deterministic finite automata: Is this answer: bbbb, bbba, bbab, bbaa, b, a correct?
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Regular Expression Similarity Check

I was solving Formal Language and Automata Theory for a competitive exam, whence I came upon this following question: The regular expression 0*(10*)* denotes same set as: 0(0+10)* (0+1)10(0+1) ...
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What does q-prime ($q'$) actually mean?

I'm learning about finite automata right now, and struggling with a bit of the math notation. In the explanation here: http://math.stackexchange.com/a/563875/125649, the user explains that the ...
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Prove or disprove that the language $L_1 = \{a^nb^m \mid n < m \}$ is regular

I have possible strategy for a proof that it is not regular. I am wondering if it is valid. Step 1: Prove that the language $L_2 = \{a^nb^n\}$ is not regular (for example with the Pumping Lemma). ...
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Proof that suffix of $ab$ needs at least 3 states in NFA

I need to prove that for an NFA that accepts all languages $L(M)=\{w \in \{a,b\}^* \mid wab \}$ with a suffix of $ab$ needs at least 3 states. The smallest automata would look like this: $\to(s) \to ...
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29 views

Create a general NFA for $M_n$

I need to create a general NFA $M_n$ where $n \in \mathbb{N_0}$ with the following language defined: $$L(M_n) = \left\{ w \in \{0,1\}^* \big | x1y \textit{ for } x \in \{0,1\}^* \textit{ and } y \in ...
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Turing machine true/false questions

There is a non-regular language that is recognized by a Turing Machine. I believe the answer to this is true, because Turing machines can "count" computations and ...
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47 views

Proof by pumping lemma

Let's say that we have to prove that $L = \{ww^Rv |w,v\in \Sigma^*\}$ is irregular. I would take a string such that $w = baba^m$ and $w^R=a^mbab$ and $v = a$ and then I would pump divide $w$ into ...
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Determining a language with a Turing Machine

How can I build a Turing Machine that determines the following language? $$L_{E - DFA} = \{\langle A \rangle | \text{$A$ is a $DFA$ and $L(A) = \varnothing$}\}$$ Thanks alot
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Why isn't this a sufficient proof?

So basically, we have a question that asks us to prove that given a particular Deterministic finite automaton (DFA), there is a symbol for which we can get to a state $q$ from a state $p$ given a ...
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If $s \geq 3$, $3$ divides $s$, and $t = s/3$, then $t+1 < s$.

I am using the pumping lemma to prove a language is not regular, and would like to assert what I have stated in the title of the question to complete my proof. That is, if $s \geq 3$, $3$ divides $s$, ...
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138 views

Prove that a PDA with accept states accepts all context-free languages

Or in other words that $\forall L: L \in DCFL => L \in CFL$. First of all, does this statement even require a proof? My idea was to let L be an arbitrary language, such that $L \in DCFL$, this ...
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proving regular language

let $L$ be a language over the alphabet $\{a,b\}$ that maintains that for each $w \in L$ ,the difference in absolute between the number of apearences of the letter $a$ and the number of apearences ...
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Question about second condition of pumping lemma

I don't think that I fully understand how to use the pumping lemma to prove that a given language is not regular. I'm reading Sipser and according to him the definition of the pumping lemma is: "If A ...
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50 views

Showing a grammar to be ambiguous

I'm learning about grammar ambiguity and trying to show the following grammar is ambiguous: $S \rightarrow ScS | SdS | A$ $A \rightarrow a | b$ I used 2 different left-derivations to get the same ...
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Grammar into Chomsky Normal Form

Convert the following grammar into Chomsky Normal Form (CNF): S → aS | aAA | bB A → aA | λ B → bB | aaB I think this looks ok, but not sure. Maybe someone can point out where I go wrong: ...
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57 views

Construct an automaton by using sliding window method

Given alphabet $\Gamma = \{0,1\}$, let $L = \{\omega : All\ words\ ending\ 010\}$ be a language. Find an automaton. I have to find an automaton using sliding window method.. First I need some ...
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289 views

Show that a language is not regular using Myhill-Nerode Theorem

I'd like to show that the language below is not regular using Myhill-Nerode Theorem. How can I do that? Let Σ = {0, 1}. Let L = {ww|w ∈ Σ*} I am not sure where ...
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69 views

Constructing regular grammar

I'm trying to make a regular grammar for this language: $$ L = \{ a^ncb^m(cc)^p : n\ge 1, m\le 1, p\ge 0\} $$ Where the alphabet is $ \Sigma = \{a,b,c\}$ It seemed like right-linear. This may be ...
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context free grammar design

Design a context free grammar and PDA for the following language. $$\Sigma = \{0,1\},\qquad L = \left\{uv \mid u \in \sum^{*} \;v\in \sum^{*}1\sum^{*} \text{ with }|u| \geq |v| \right\}$$ I'm not ...
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56 views

$2^E$ where $E$ is a set

I'm studing the definition of automaton $G=(X, E, f, \Gamma, x_o, X_m)$ where $X$ is the set of states and $E$ is the set of events. My sources report that $\Gamma:X \rightarrow 2^E$ is the indicator ...
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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 ...
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Proving what are the equivalence classes of the relation $R_{L}$

I tried writing a solution for a question that defined a language $L$ and asked to find the equivalence classes of the relation $R_{L}$ The TA wrote that "this is not what you should prove" (or "this ...
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52 views

Legal actions on a PDA and terminology

I am unsure about the following so I would like to verify if my statements are true: We can remove at most a single character ($Z\in\Gamma$) from the PDA (top ?) of the stack with one step of the ...
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47 views

Given two NFAs, is there a way to figure out if there exists a language that works for both of them?

Given two non-deterministic finite automaton, is there a way to determine if there exists a single language that satisfies them both?
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A question about the regular languages being closed under Boolean operation (how to generalize)

I know that if $L_{1},L_{2}$ are regular languages then so is $L_{1}\cap L_{2},L_{1}\cup L_{2}$ are regular languages, I also know that $L$ is regular $\implies L^{c}$ is regular . It is easy to ...
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84 views

How to prove that the language of a DFA is some $L$

Consider the following DFA: It is quite clear that the language of this FDA is all the words that don't have the word $aa$ as a subword. My question is: How can I formally prove that this is the ...
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Different version of pumping lemma and how to prove it

I have a question to solve but I am not even getting a direction to start or how to narrow down this problem. Please provide in your inputs. Consider the following version of pumping lemma. For any ...
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461 views

String matching automata preprocessing

I have an alphabet A = {a,b,c} and a pattern P = "abcaab". The task is to build a finite automaton of the transition function (delta) for {0,6} (the length of the pattern) and each element of the ...
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How can I prove that this language is regular?

Given a language $L$, define the language $K$ as the language $L$ where every second character is replaced with a $\#$. (Note: $\#$ is not part of the alphabet of $L$.) For example, if $L = \{ab, ...
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1answer
19 views

Push Down Automata that recognizes language

I'm struggling on how to use the stack for this push down automata problem. The problem is to design a PDA that recognizes the language: $$A = \{a^ib^{2i}|\,i>0\}$$ So, we will be pushing a's onto ...
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Designing a deterministic finite automata

How would I go about designing a deterministic finite automata to recognize the language L = {λ, ab, abab, ababab, . . . } consisting of strings that start with ‘a’, end with ‘b’, and alternate in ...
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80 views

Input and output of a Turing machine

For some machine models of computation there is no question what their input and output is: it's just the contents of some specific "cells", e.g. on a "tape" isomorphic to $\mathbb{N}$. Consider for ...
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1answer
16 views

Use the power-set construction to find a deterministic automata

Given a nondeterministc automata N, how do you use the power-set construction to find a deterministic automata that recognizes L(N)? Here is my work so far: We can start in state 1, 2. If we get ...
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Soft question, Understanding NFAs and DFAs; Requirements for either.

I have a few quick questions about NFAs and DFAs. Is any automaton with epsilon transitions always a NFA? Is any automaton with two paths for the same symbol from a state always a NFA? Ex. Say state ...
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29 views

Is there a fast way to know whether a language is regular or not?

Or at least have an idea? Because I can't see whether a language is regular before I can disprove it by pumping lemma and it takes me like a hour to try to disprove.
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using pumping lemma to prove that a set is not regular

A={s11s|s $\epsilon$ {0}^*} so the strings 00011000 and 000001100000 are accepted of A but not 00100 or 001100000. Demon chooses k. ...
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80 views

How to convert this NFA to DFA?

http://www.cs.odu.edu/~toida/nerzic/390teched/regular/fa/figures/nfa-dfa1.jpg What are the steps for convert this NFA to DFA??
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Using the Pumping Lemma to prove a language is not regular.

I want to know if my proof is wrong and whether what I am doing works. $$\sigma = \{0, 1\}$$ $$A = \{0^n1^m \mid n < m\}$$ Claim: A is not regular. Proof: Assume A is regular. Let p be the ...
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25 views

Question about Notation in a Regular Language

I am a little confused about the following notation: $L' = \{xy|x\in L \ , y\in L^R\}$. I think this expression is not equivalent with palindrome but I am not entirely sure. For example, I think the ...
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find a regular expression and FA that each define L1 ∩ L2

from the following pairs I am trying to find a regular expression and FA that each define ...
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23 views

How can I show ithat a language is regular?

I have a very quick question about regular languages, I think $\{a^{2n}| n\geq 1\}$ is regular. I do know that pumping lemma can be used to show something that is not regular. I am wondering what ...