Questions tagged [pushdown-automata]

Questions about state machines with a single stack for memory. They characterize the class of context-free languages.

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499 views

How Intersection of Regular Language and a CFL is a CFL?

CFL is not closed under intersection. That means, if we have L1,L2 of CFL then L1 intersection L2 is not a CFL And we know, all Regular languages are CFL. Then ...
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80 views

What is the strongest arithmetic theory decidable by a DFA, DPDA or PDA?

It is known that WS1S can be decided by a DFA. Is this the strongest arithmetic theory decidable by a DFA? What happens when the automata class is extended to include DPDAs or PDAs?
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56 views

Deterministic pushdown automaton for a given language

I am trying to make a deterministic pushdown automaton from this language but without success. Here is the language definition: $\ L=\{0^n 1^m a^i b^j \ /\ m,n,i,j > 0 \ and \ m+n=i+j \} $ ...
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1answer
527 views

Why no DPDA can accept Palindrome? (according to this proof)

This proof is from the book "Introduction to Languages and the Theory of Computation" by John C. Martin. My question is from the pink part at the second page: It follows in particular that no ...
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2answers
105 views

Can a Non-Deterministic Pushdown Automaton recognize $ \# a^nb^{2^n} \# $ which a TM can?

$ \# a^nb^{2^n} \# $ such that • The alphabet of the machine is {, a, b, x}. • The symbol x will never appear on the input a. • The contents of the tape at completion may be anything. • The head ...
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1answer
547 views

Creating a Deterministic Push-Down Automaton for the Union of two languages

Suppose, we have $L_1:=\{w\in\{a,b\}^*\mid \#_a(w) \equiv 0 \mod 4\}$ and $L_2:=\{w\in\{a,b\}^*\mid abaab \text{ is a substring of } w\}$. Now we want to create a Deterministic Push-Down Automaton for ...
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54 views

Prove that any PDA/CF language with 1 character is regular [duplicate]

I know there is a post like this already posted, but I didn't quite understand the proof. Can someone explain it to me? Thanks in advance.
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1answer
141 views

Why can’t you simulate a Turing machine with a one-stack PDA by messing with the stack?

I have heard that a matrix can be modeled as just an one array by declaring increasingly large spaces to be from the second array, and that the least you need for a Turing machine is just a PDA with ...
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1answer
180 views

Does this argument prove CFLs are not closed under union?

Context free languages are not closed under complementation. This follows from their property of non-closure under intersection: If CFLs were closed under complementation, then they must have also ...
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0answers
140 views

Is the following PDA a DPDA or NPDA?

Let the language be : $$ L = \{ w \in \{a,b\}^* : \#_a(w) = \#_b(w)\}. $$ Now the PDA that I've designed for this language and seen at many other places is : ...
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68 views

Pushdown Automata for number of a less than 2 times number of b

Suppose we want to design a pushdown automata for $L=\{x \in \{a,b \}^{*}:|x|_a<2|x|_b \}$, can anyone check whether my automata works? we have 4 states $\{q_0,q_1,q_2,q_3 \}$, three stack symbols ...
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1answer
250 views

Is Half - Palindrome subset of a context-free language context-free?

Suppose we have $L$ being a context-free language. Let $L'=\{x \in \Sigma^* | xx^R \in L \}$, is $L'$ context-free as well? I know that if $L$ is regular then $L'$ is regular as well by constructing a ...
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2answers
2k views

Proving the decidability of whether a CFG generates a particular string or not

Let $G$ be a context-free grammar and $w$ be a string of length $|w| = n$. Consider the language $A_{CFG}$ = { <$G$, $w$> | $G$ is CFG that generates $w$ }, where <$G$, $w$> is a string ...
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1answer
261 views

Can you create a deterministic PDA for non-palindomes?

Using non-determinism to create a PDA to recognize non-palindromes is easy. My first instinct was to say yes, but it would be extremely complicated. After thinking about it, I don't think you could.
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332 views

Constructing a PDA to accept the language {a^i b^j c^k where i,j,k>0 and i<=j<=2k}

Can anybody help me out with this? If I try to compare $a$'s with $b$'s to check if $j\ge i$ then I won't be able to compare the same number of $b$'s with the number of $c$'s that is to check if $j\le ...
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148 views

Pushdown Automata - constructing a PDA to recognise a language with at least as many as as bs

I am trying to construct a 3-state PDA to recognise (I need to create a transition diagram for this question) ...
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1answer
346 views

Pushdown Automata - can you have multiple transition functions options between 2 states?

I was wondering if you have 2 states, lets say q0 and q1. Are you allowed to have multiple options to transition between these 2 states? For example, ...
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2answers
46 views

DPDA for $\{1^ky \mid \text{$y\in \{0,1\}^*$ with $|y|_1 \le k$ and $k \in \mathbb N: k\ge1$}\}$

I need some help with the following task: I have to construct a DPDA for $\{1^ky \mid \text{$y\in \{0,1\}^*$ with $|y|_1 \le k$ and $k \in \mathbb N: k\ge1$}\}$. How can I recognize that the new ...
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1answer
762 views

Pushdown Automaton to accept all strings such that no prefix has more 1’s than 0’s

Design a Pushdown Automata, accepting either by final state or by empty stack to accept the set of all strings of 0’s and 1’s such that no prefix has more 1’s than 0’s This is a homework question,...
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What is the class of automata with stack and unlimited amount of memory, addressable only by immediates?

Let's assume we've got an automata with infinite stack ($s_n \epsilon \mathbb{Z}$) and infinite amount of "registers", but no arbitrary memory access whatsoever and it's data is separated from code. ...
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3answers
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Context-free grammar of the concatenation of a string S and subsequence of reversed S

I have to find a Context-Free grammar that generates the language: $L_1 = \{x\#y\ |\ y$ is a subsequence of $x^R$, and $x\in\{a,b\}^*\}$, $\Sigma=\{a,b,\#\}$ The concatenation of two mutually ...
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1answer
903 views

A push-down automaton with two stacks which is equivalent to a linear-bounded automaton

It is known that a PDA with two stacks is equivalent to a TM. On the other hand a PDA with one stack is capable to recognise only context-free languages. Hence there is a kind of a gap between the ...
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1answer
214 views

It is decidable whether a pushdown automaton will accept a word? [duplicate]

I'm asking myself if the problem of decide whether a push down automaton will accept a word is decidable. I would say that you can simulate a push down automaton with a Turing Machine and, if it ...
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2answers
513 views

L(M)=L where M is a TM that can move right or stay, so L is decidable

Suppose that L(M)=L where M is a one tape TM that can move right or stay. I need to Show that L is decidable. I thought of reducing a PDA to this TM, since moving to the right is equivalent to ...
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1answer
117 views

Are the languages recognized by deterministic one-counter machines equivalent to deterministic context free language?

In Introduction to Automata Theory, Languages, and Computation, John Hopcroft mentioned[1] In fact the languages of one counter machines are accepted by deterministic PDA's although the proof is ...
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65 views

How to visualize non-deterministic pushdown automata?

My friend and I are working on this project for our Formal Languages and Automata class that consists in building a pushdown automaton. A part of the project that is bothering me is how to visualize ...
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1answer
189 views

Is the halting problem solvable for NPDAs?

After the total silence in response to my last question, I am rethinking my assumptions. DPDAs are, of course, solvable, and I believe that their loops can be found in the manner I described in my ...
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1answer
146 views

Proof emptiness for PDA is $\mathcal{O}(n^3)$

It is well known that the emptiness problem vor PDAs is in $\mathcal{O}(n^3)$. I couldn't find a good paper proving this theorem. Furthermore a proof for VPAs would be fine for me as well if that is ...
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67 views

Find PDA for CFL = {x#y | |x| = |y| and x ≠ y} [duplicate]

I am studying push down automata. When I read a solution for showing $L = \{x\#y \mid x \neq y, x,y \in \{0,1\}^*\}$ is a CFL, I could understand $L = L_1 \cup L_2$, $L_1 = \{x\#y\mid|x| \neq |y|\}$, ...
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Detecting loops in NPDAs

I'm aware that the halting problem is solvable for PDAs, but I have recently discovered that I am wrong about how to actually do it. I used to think that you could detect an infinite loop by meeting ...
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1answer
395 views

Constructing PDA to accept language { 0^i 1^j 2^k | i = 2j or i = k, where i,j,k >= 1 }

$L = \{ 0^i 1^j 2^k \mid i = 2j \text{ or } i = k, \text{ where } i,j,k \geq 1 \}$ I have trouble about this PDA. Anybody can help me about draw this PDA?
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1k views

aⁿbⁿcⁿdⁿ using 2-stack PDA

I need to construct a PDA using 2 stacks for accepting the language $L = \{a^nb^nc^nd^n | $ $n \geq 0\}$. Pushing $a$'s to first stack and $b$'s to second and poping them for corresponding $c$'s and ...
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1answer
218 views

Pushdown Automata for words x#y where x and y are different words over {0,1} that share one similarity

I was instructed to create a pushdown automaton described in the title. Basically, the pushdown automaton accepts strings of the form $x\#y$ where $x$ and $y$ are strings of 1s and 0s such that there ...
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41 views

kPDA handling multiple epsilon transtions

I'm assigned to build a kPDA with 2 stacks that handles {w#w, where w is a string of (0,1)*}. I understand the # delineates the two strings, but I'm unsure of the logic when popping off stacks with ...
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25 views

Automaton without stack for visibly pushdown languages

This paper here describes an alternating automaton which can recognize visibly pushdown langauges without using a stack. Unfortunately the transformation from NVPA to such an automaton is skipped in ...
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1answer
32 views

Behavior of specific PDA for a certain input

Suppose we're given the non-deterministic PDA shown below which reads from the alphabet $\sum = \lbrace a,b \rbrace$. How will this PDA behave if we pass it the string $ba$? We read $b$ first and push ...
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197 views

How can I find a language from a given PDA

I have the following PDA: And a given solution for his languages ${L}_{\mathrm{End}}(M_2)$ and ${L}_{\mathrm{PDA}}(M_2)$ with $ \mathrm{L}_{\mathrm{End}}\left(\mathrm{M}_{2}\right)=\left\{\mathrm{a}^{...
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1answer
101 views

Make a Pushdown automata that accepts a language defined by strings that contain the same number of a and b [duplicate]

How do I build a pushdown automata that accepts the language over the alphabet $\Sigma = \{a, b\}$, defined by the strings $w$, such that $|w|_a = |w|_b$? I'm sorry I can't give any approach of what ...
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1answer
70 views

How construct PDA to $L = \{x \in(a,b,c,d)^* \mid -10 \leq ( |x|_a + |x|_b) - ( |x|_c + |x|_d) \leq 10 \}$

$L = \{x \in(a,b,c,d)^* \mid -10 \leq ( |x|_a + |x|_b) - ( |x|_c + |x|_d) \leq 10 \}$ I don't have any idea. Can someone help me.
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441 views

Prove $ L = \{ww^{R} \in \{a, b\}^{*} : |w|_{a} \equiv |w|_{b} \equiv 0$ $ (mod$ $13) \} $ is regular or context-free or neither

$ L = \{ww^{R} \in \{a, b\}^{*} : |w|_{a} \equiv |w|_{b} \equiv 0$ $ (mod$ $13) \} $ Exercises: If the language L is regular (build a DFA or regular expression) else if the language L is context-...
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1answer
85 views

NPDA transitions to different states by taking same input and popping same top element of a stack

Suppose i have some NPDA and there is some transition functions defined as: $\delta(q_{1},a,A) = (q_{2}, A)$ $\delta(q_{1},a,A) = (q_{3}, Z)$ Is it allowed? I understand, that since the NPDA is ...
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2k views

Turing machine VS Push Down Automaton in CFL

I want to ask that between turing machine and pushdown automaton: which abstract machine can handle context-free language (CFL) in a more efficient way, and why? I know that a pushdown automaton can ...
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1answer
784 views

Allowing an empty (epsilon) transition in a PDA

I'm trying to allow an empty transition in a PDA for the following language: Alphabet: $Σ = \{a, b, c\}$ Language: $L = \{ a^ib^j \mid i \neq j \} \cdot \{ c \}^\ast$ Examples of words in $L$: $\...
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1answer
250 views

PDA for the language of strings containing the same number of a and b

Need idea for solving the following pushdown automata: $\mathcal{L}=\{w\in\sum ^* | \#a(w)=\#b(w),|w|\geqslant 0\} \,\,\,\, \sum=\{a,b\}$ In the beginning I thought to PUSH A for input a, and then ...
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1answer
2k views

Constructing a PDA with an unequal number of a/b

I'm looking at this pdf for problems: http://www.public.asu.edu/~ccolbou/src/355hw5solf10.pdf I found question 3g to construct a pushdown automata for the following: {$ {a^i b^j}$ | ${i \neq j}$} ...
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1answer
65 views

How to prove that if $L, G$ are regular languages then $\{w\in L|\exists x\in G: |x|=2\cdot |w|\}$ is a context-free language?

Prove that if $L, G$ are regular languages over $\{a,b,c\}$ then $H=\{w\in L|\exists x\in G: |x|=2\cdot |w|\}$ is a context-free language? I think this could be a good exercise and the conditions are ...
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1answer
50 views

Grammar of words with exactly $k$ prefixes in another grammar

Given a context-free grammar $G$, how can one systematically construct a grammar $G_k$ such that $$ L(G_k) = \{w \in \Sigma^* : |\text{Pref}(w) \cap L(G)| = k\} $$ where $\text{Pref}(w)$ is the set ...
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1answer
385 views

Constructing PDA to accept language $\{a^ib^j \mid 0 \leq j \leq 2i\}$

How can I construct a PDA which accepts the language $\{a^ib^j \mid 0 \leq j \leq 2i\}$?
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2answers
535 views

Does left factoring CFG make it unambiguous?

I came across following problem: If the CFG is left factored then it must be Unambiguous and Not left Recursive. TRUE/FALSE? I have many thoughts about this. But I feel they are somewhat ...
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1answer
583 views

Who first introduced the pushdown automaton?

I'm interested in learning more about the history of automata theory and have tracked down many of the original papers on Turing machines, finite automata, and the like. However, I'm having trouble ...

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