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

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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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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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21 views

Finding Kth string by applying given operations

Given is a matrix of dimension 4*4 in which we are given the result when value along row is computed with value along column. ...
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13 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
43 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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34 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
36 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
58 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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27 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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Pumping Lemma & Regular Language

For each regular language L, we have an integer k such that: ...
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1answer
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
38 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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42 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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25 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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17 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 ...
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69 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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32 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
25 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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31 views

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
66 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
36 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
28 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
70 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
70 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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30 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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38 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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52 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
18 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
90 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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2answers
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.
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1answer
31 views

What did the proof by diagonalization actually disprove?

http://www.cse.ohio-state.edu/~gurari/theory-bk/theory-bk-fourse5.html I sort of understand the proof, but is it showing that some language are undecidable? If so, what language exactly? Because each ...
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CFG Convertion to GNF

I have a very simple CFG that I am trying to convert into GNF. The CFG is: S -> aSbS S -> epsilon I looked at the CFG and I think I can just do the ...
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1answer
28 views

Backus-Naur Form with automata

Parsers & compilers usually utilize deterministic finite automata to parse input. It's very easy to implement a generic DFA tool, that simulates any DFA table for example to validate input. ...
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39 views

turing machine accept and reject state

I am pretty new to Turing Machines and I am trying to understand the basic things first...so my question is , would this machine accept all words ending in 'a' ? if ...
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24 views

Regular expression translation.

Given a set {1,2,...9} how can I construct a regular expression starts with a 3 has no 8's and has even number of 6's? Here's what I tried: $$$$ Define a new set no8 = {1,2,3,4,5,6,7,9} ...
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1answer
29 views

having hard time reading symbols in this Turing Machine

I am reading few books and I am looking at different examples of a Turing Machine, and I am getting frustrated reading symbols especially in this example...What does ...
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how do I make this post machine accept aab or baa?

so far I made it accept, a, aaa,bab but now I want strings aab or baa. How would I do this ? this is what I have so far... edit: @Hagen von Eitzen here is the example of Post Machine that a lot of ...
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Is the language $L = \{0^m1^n: m \neq n \}$ not context free?

I have been trying to prove that this is not a context free language using the pumping lemma for CFLs. I have tried for hours but am not able to prove it. Is it a context free language or not? How to ...
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Regular Expressions Help [duplicate]

I need a little help with Regular Expressions. The allowed operations are obviously + (union) , * (Kleene star) and concatenation. I have to write Regex for the following 2 examples. I have tried a ...
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DFA Construction with three strings in language

Draw DFA that recognizes the following language, with the alphabet {0, 1} {0011, 11, 0101} I'm having a lot of trouble with this, because I know DFA have to have a determined path from each state ...
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1answer
37 views

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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Is this DFA correct?

I am reviewing. I need to write a DFA that accepts a string w such that bab is not a substring. Is there any error. Also, any guideline or tips? Since it's a DFA I don't make more than 2 ...
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How to construct NFAs that recognize the following languages.

I am new to this computation theory and I am trying to answer the following question. Can you please check if I am on the right track? If there is any material that I can study for problems like ...