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

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How can a DFA corresponding to an NFA have a transition that the original NFA does not?

First sorry for the poor pictures, but I think they are ok enough to get the point across. I would like to see the steps involved to convert this NFA to a DFA using the method explained in this ...
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1answer
8 views

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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21 views

DFA for language accepting odd number of a's and each a followed by at least 3 b's

I am creating a DFA for a language (over alphabets {a,b}) that accepts all strings containing "odd number of a's and each a followed by at least 3 b's" . This is what I've gotten so far with q4 as the ...
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2answers
16 views

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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18 views

Is a DFA a subset of NFA? Why?

After reading this previous question Difference between NFA and DFA, it's clearer to me their relationship/differences. Can one say that a DFA is a subset of a NFA where both recognize a/the same ...
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19 views

A language recognizes by a DFA

So the solution in problem 1.61 in this file http://bsd7.cs.sunysb.edu/~stark/CSE540/Handouts/hw1_notes.pdf uses an argument of the form: "$M$ is a DFA that recognizes the language $C$. Because the ...
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35 views

Number of states of a finite automaton recognizing all words beginning with some fixed string $x$

For a string $x \in \{a,b\}^\ast$ with $|x| = n$, how many states are required for an FA accepting the language of all strings in $\{a,b\}$ that begin with $x$? For each of these states, describe the ...
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1answer
7 views

Find a state machine or a regex that accept the following language description

The alphabet of the language L is {a, b} and there has to be an even number of both a's and b's but no other restrictions apply. I've been at this for over an hour, drawing state machines that lead ...
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38 views

FA that accepts only those words that have an even number of substrings cdc?

I take this question as it could accept cdccdc,cdccdccdccdc,dddcdccdc,etc. I feel that I coveed all the even loops of cdccdc but I am stuck trying to figure out how to add in c* and d* in the mix of ...
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40 views

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

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

Turing Machine Problem

We know, A Turing machine is a hypothetical device that manipulates symbols on a strip of tape according to a table of rules I Draw a TM for input $x=(0+1)^*$ i want to implement ...
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1answer
19 views

$L=${$a^nb^nc^n : n \geq 0 $} CFG Recognizing

Suppose $L=${$a^nb^nc^n : n \geq 0 $} and I. $h(L), h(a)=a, h(b)=bb, h(c)=b$ II. $L^R$ III. $L^*$ IV. $h(L), h(a)=a, h(b)=bb, h(c)=a$ Why just I is a CFG and other is not? anyone can help me to ...
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1answer
39 views

Basic Question about ambiguity of Grammar

I saw one book in Computation Course. I take a picture from this book, and in this book say why (or not) the following grammar is ambiguous? I couldn't find any solution to prove it's ambiguous. ...
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1answer
34 views

Language of a grammar vs regular expression vs 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 ...
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1answer
20 views

context free grammar that describes even numbers

I am learning about context-free grammars and as a toy example I wanted to design one that describes binary digits ending with 0. My attempt : S -> 1S | 0S | e0 - where e is the empty string. Is this ...
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1answer
38 views

PDA and Some language Grammar inference

L1={$w^* $| w=x and $ x \in \Sigma^*$} L2={$ww^R ww^R $| $ w \in ( \Sigma + \Sigma)^*$} L3={$w | w=xy, x,y \in \Sigma^*$, y is a substring of x} a) there is a PDA(push down automata) that accept ...
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1answer
31 views

Pushdown Automata and Challenge in Grammar

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$\epsilon$ ...
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22 views

Lattice worms with nontrivial deaths

In Paterson's worms, a triangular lattice is used. A worm can move in 6 directions. As each node is hit, the worm follows an internal rule for which edge it will eat next based on the edges already ...
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1answer
48 views

Regular Language and Unknown Operation

I read the $L$ is a Regular language. Define $L'$ as following: $$L'=\{a_2a_1a_4a_3\ldots a_{2n}a_{2n-1}\mid a_1a_2\ldots a_{2n} \in L\}.$$ why $L'$ is Regular? any hint or idea would be highly ...
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36 views

Every DPDA has an equivalent DPDA that always reads the entire input string

I am trying to understand the proof from Michael Sipser's Introduction to the Theory of Computation, page 132. I don't understand why if $q \in F′$ then $\delta(q,a,\$)$ is set to ...
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1answer
40 views

A CFG Grammar for One Language

Suppose : $w_1,w_2 \in \{a,b\}^∗$ and $ L=\{w_1w_2 \mid w_1,w_2 \in \{a,b\}^* \land n_a(w_1)=n_b(w_2)\}$ $n_a$ is number of $a$'s and $n_b$ is number of $b$'s. This is a Entrance Exam question. I ...
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1answer
60 views

Challenge on Property of Complement in Language

We have: and M be a finite automata. Suppose d(M) be a deterministic automata that equivalence to M. if $M_1$ and $M_2$ be two finite automata, $M_1 + M_2$ is the finite automata such that the ...
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32 views

Language of Specific Grammar

I ran into this exercise in Sipser's Note on Computation Theory. Consider the following grammar $G$: $$\begin{align} S &\to aSD \;|\; bB \\ D &\to dS \;|\; a \\ B &\to bB \;|\; ...
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15 views

Algorithm that takes input desc. of two PDAs and outputs intersection of langs. recognized by two PDAs

Does there exist an algorithm which takes as input the descriptions of two pushdown automata, $P1$ and $P2$, and prints the description of another pushdown automaton which recognizes the intersection ...
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1answer
17 views

Deciding TM which fails to halt whenever the length of its input string is a prime number

I have the following Statement: "A TM called $A$ which fails to halt (i.e runs forever) whenever the length of its input string is a prime number, and eventually halts for all other input strings" ...
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1answer
21 views

disproving union of infinitely many regular languages

I want to disprove the following statement: "if $L$ is the union of infinitely many regular languages, then $L$ is guaranteed to be a regular language." I don't know where to start. Any hint will be ...
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1answer
49 views

Complex automata Rubiks cube question (with picture) help needed

Question 1 A Rubik’s Cube is a puzzle in the shape of a cube. Each face is covered by nine stickers, each of which is coloured with one of six colours: white, red, blue, orange, green, andyellow. An ...
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44 views

predicate logic with assumption NP $\neq$ CO-NP?

Anyone could describe why: Set of All Tautology in propositional logic with assumption NP $\neq$ CO-NP is CO-NP Complete. Thanks. I ask it here before: Is the language of tautologies NP-complete? ...
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26 views

Design an finite automata for 010 and 01? [duplicate]

I have tried below question for designing automata but didn't success . ...
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1answer
72 views

$NP^{PP} vs. PP^{NP}$, which one subsumes the other?

I understand why P with an NP oracle ($P^{NP}$) subsumes $NP$: because it contains co-NP. But how about NP with a P oracle? Can it be any different from NP? (I'm guessing they are the same otherwise ...
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What are the classes in A.N. Maslov hierarchy of indexed languages corresponding to Chomsky Hierachy?

As we know,that classes in A.N. Maslov hierarchy of indexed languages of level 2 is in sensitive languages of Chomsky hierarchy. What are the classes in A.N. Maslov hierarchy of indexed languages ...
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20 views

Do automatons and formal grammars belong to formal systems

A formal system consists of a formal language, a formal grammar that generates the language, a set of axioms, and a set of inference rules. Are automatons also formal systems? Is an automaton ...
3
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1answer
71 views

Exponential objects in a category of abstract automata.

I'm working with a more or less standard definition of the category Aut(C) of automata over a category C (where C has finite products) which has tuples $$ A=\langle I_{A},O_{A},S_{A},\sigma_{A}, ...
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52 views

How to check whether a language is regular or not?

Say I have a given expression like $L_1\{a^n\mid n\ge0\}$ $L_2\{b^n\mid n\ge 0\}$ Then what is the procedure of checking weather L1.L2 is regular or not?
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1answer
27 views

How does the push-down automaton have to look like?

Could you give me a hint how to find a push-down automaton for the language: $$L=\{ a^n b^{2n} | n \in \mathbb{N}\}$$ How does the push-down automaton have to look like?
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2answers
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NFA for $L = \{ w \in \{a,b,c\}^* : \text{at least one symbol appears only once in }w \}$

Write an NFA to recognize the language $$L = \{ w \in \{a,b,c\}^* : \text{at least one symbol appears only once in }w \}.$$ I'm not quite sure how to do this question. I don't know how to keep ...
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1answer
72 views

Turing machine for the language a^nb ^2nc^3n

How can we give a Turing Machines that accept following language. $$a^nb^{2n}c^{3n}$$ I am allowed to use also pseudo-code descriptions (i.e. high level descriptions of movements of r/w head):
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1answer
38 views

Deterministic Push-Down Automata

Does there exist Deterministic Push-Down Automata for the language below. Any kind of answer will be highly appreciated! $$L =ba^nb^n U bba^nb^{2n}$$
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Struggling to prove Markov chain property / State machine property - I can see what I need to do just can't write it

First notation, I have created the shorthand: $$P_x(A)=\mathbb{P}(A|X_0=x)$$ just to save time. I wish to prove "Lemma 1.3" which states the following: If $0<\alpha\le P_x(T_y\le k) \forall x\in ...
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1answer
24 views

Stack automata with nonequality

I encontered the following problem that I'm unable to solve. The goal is to construct a stack automata, that accepts language $$ L = \left\{u\mathrm{\underline{c}}v \mid u,v \in ...
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2answers
30 views

Turing Machine Decidability

I have been working on this problem for few hours, but haven't been able to come up with a solution : Is the following problem decidable? Given a TM M, whether there is a w such that M enters each of ...
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1answer
72 views

An algorithm that minimises the number of states for a conversion from a DFA to an NFA

I am looking for an algorithm that can convert from a DFA to an NFA, while at the same time producing the minimum number of states for the NFA. My gut tells me this can be done with around $n$ ...
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2answers
96 views

pumping lemma: ww^R not regular

I'm trying to prove that $L = \{ww^R : w \in \{a,b\}^*\}$ ($w^R$ is the reverse of $w$) is not regular using the pumping lemma. Let $p$ be the pumping length and $s = a^pbba^p$. $x = \epsilon$, $y = ...
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1answer
32 views

Checking my CFG to CNF answer

I attempted to transform the given CFG into CNF. $$S → ASA|A$$ $$A→aa|ε$$ Here are my steps: $$S→X$$ $$X→XA|AX|A$$ $$A→aa$$ $$S→X$$ $$X→XA|AX|YY$$ $$A→YY$$ $$Y→a$$ $$S→XA|AX|YY$$ ...
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42 views

Create a finite-state machine

I need to create a finite-state machine which accepts strings whose characters are in {a,b,c} and produce output strings of T's and F's. The machine outputs a T once the characters ab is encountered ...
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1answer
22 views

minimal DFA with four states

I want to minimal this DFA: But i don't know what to do. Anyone can help me? Thanks
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57 views

Proving context free language membership is $P$ complete with respect to log-space reductions

This is exercise from Introduction to Automata theory, Languages and Computation, by Hopcrof, Ullman (first edition). I found example of polynomial reduction to some problems in logic, or graph ...
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1answer
22 views

Decide whether DFA accepts all Strings

Wikipedia : Because DFAs can be reduced to a canonical form (minimal DFAs), there are also efficient algorithms to determine: whether a DFA accepts any strings. whether a DFA accepts all strings. ...
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1answer
93 views

Can you draw the e-NFA from the following definition?

I am trying to understand the solution, because I think I got it completely wrong. I wrote we could take the initial DFA and replace the normal transitions with epsilon transition except for all ...
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28 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.