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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When our two-state PDA constructed from CFG is non-deterministic PDA?

We can always convert our GNF-CFG/CNF-CFG to a two-state PDA but i'm wondering when our PDA is non-deterministic? i'm sure we can not make DPDA for non-Deterministic-CFL , and i suspect that same rule ...
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How to find the language and create Push down automaton if the A is continuously looping ? and will PDA accept L produced without A

Let us consider the following Context-Free Grammar G = ({S,A,B,C,D},{a, b}, S, P) with production rules P: S → SSA | Bb A → BSA B → A | Cb C → AD | Cb | ɛ D → a | b | ɛ Let L be the language ...
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Construct a PDA that recognizes the following language: L={uawb: u,w ∈ {a,b}*, |u|=|w|}

I am having trouble finding the PDA with 1 state for this one. So far my solution is this but i cant figure out how to get to 1 state. Alphabet: {a, b}, Stack alphabet (the first symbol is the ...
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PDA with more than one initial state

I'm wondering if PDAs with more than one initial states are also accepting context free languages. If found that question on this site about NFAs and would like to know if this answer is also valid ...
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Are DPDAs accepting on final state equivalent to DPDAs accepting on empty stack equivalent? [duplicate]

Say I have a string x that is accepted by some DPDA P that accepts empty stack. Intuitively it's seems impossible for P to accept any string x.y for any y != epsilon. The below DPDA accepts on final ...
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$\mathcal{G} = \{ v_2 v_4 \ldots v_{k} : v_1 v_2 v_3 v_4 \ldots v_{k-1} v_{k} \in \mathcal{L}, \text{ $k$ even} \} $ is context free language

Let $\mathcal{L}$ be context free language over alphabet $\Sigma$. Define $\mathcal{G}$ as $$\mathcal{G} = \{ v_2 v_4 \ldots v_{k} : v_1 v_2 v_3 v_4 \ldots v_{k-1} v_{k} \in \mathcal{L}, \text{ $k$ ...
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Modify a PDA with acceptance by empty stack for it to have acceptance by empty stack

i have this PDA with acceptance by final state I made two automaton and i'd like to know if one of them is the right answer or if i'm mistaken for both 1st one: Second one: Thank you !
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Question about proof of Lemma 2.41 - Sipser book

Doesn't the modification described in paragraph three potentially introduce non-determinism? For example, say neither a, b, x, nor y is the empty string (denoted e). If in the original machine P we ...
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PDA (PushDown Automata) What is the language recognized by the following PDA?

Is this language regular? I couldn't find this language. Can you help me with this PDA question? Please explain..
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Suppose you want to define a new model of computation called a “Turing-Stack Machine” (TSM)

Suppose you want to define a new model of computation called a “Turing-Stack Machine” (TSM). The idea is that a TSM would have all the components of a deterministic Turing machine, but also a stack (...
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Formal definition of a language accepted by PDA

I am a bit confused on how to give a formal definition of the language accepted by A? I can describe it by "The language of all strings starting with n-many a's or n-many c's followed by n-many b's" ...
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1answer
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PDA for parentheses language

Construct a PDA for the language described by the following CFG: $$ S \to [S] \mid \{S\} \mid \Lambda $$ How can I develop a pushdown automaton for this language?
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PDA for $L= \{w : n_a(w)+n_b(w) = 2n_c(w)\}$

I'm pretty new to the PDA topic. How do I construct an NPDA for the language $$L= \{w : n_a(w)+n_b(w) = 2n_c(w)\}.$$ I've tried all the possibilities, but I still somehow end up accepting all words.
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How to convert NPDA to PDA?

I have been given this Nondeterministic pushdown automata and I need to convert it to deterministic pushdown automata, I have been stuck with this for a while now, I know that there cant be ...
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1answer
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How do I convert this PDA to CFG?

How do I convert this PDA to CFG? I am currently stuck with this, any help would be appreciated, thank you in advance!
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The total length of input to a pushdown automata which accepts by empty stack is an upper bound on the number states and stack symbols

I was going through the classic text "Introduction to Automata Theory, Languages, and Computation" (3rd Edition) by Jeffrey Ullman ,John Hopcroft, Rajeev Motwani, where I came across few statements ...
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1answer
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Is there a difference between the equivalent automaton of a grammar and an automaton which accepts the language produced by the grammar?

I have been assigned some homework in uni, related to push-down automatons (evaluated via final state, not empty stack) and context-free grammars. I have noticed that questions related to generating ...
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2answers
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Is it decidable for a NPDA to halt?

I know that it is decidable for an NPDA to accept a string $w$, i.e. a TM can receive as input the description of an NPDA along with a string and test if the NPDA accepts the string. But are there ...
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A pda that accepts all strings over an alphabet

If you were asked to construct a pda that recognizes all strings over the alphabet {a,b,c,d}, that is L={w | w belongs to (a,b,c,d)*} How would that be constructed? My idea is to have one state as ...
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How does a PDA compare two configurations of accepting histories?

In Michael Sipser's book, they prove that ALL_CFG is undecidable using accepting computation histories and PDAs. My question is how exactly (with details of implementation) a PDA goes on to compare ...
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1answer
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How should we interpret a transition rule $\epsilon,b\to c$ in a Pushdown Automata as Sipser defined in his book?

After defining pushdown automaton in Sipser's book at p. 113: at the bottom of p.114, he tries to describe a way to make a diagram for pushdown automaton as following: My question is about the part "...
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In a NPDA if the stack is empty, where the start/end state are the same can you go again

Thoughts I am wondering if you get a string that goes through the NPDA and arrives back at q0 can I go through the NPDA again so that the last number in the string is not fixed, or is it that once I ...
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1answer
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Find CFG for the following language

I need to show that the following language is context free: $$L = \{a^\ell b^n c^m | \ell, n, m \in \mathbb{N}^+ \wedge ((\ell \ge n) \vee (\ell \ge m))\}$$
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Determine the language of the given NPDA

Thoughts I am wondering is the language $ab^*$, since $a$ pushes $X$ to the stack and $b$ pops, and if there is an $a$ there has to be a $b$ to get back to the final state? Also, is it right to say $...
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Constructing a PDA which acceptsL {${a^i b^j c^k}$| $i,j,k≥0$ and $i=j$ or $i=k$}

I have to construct a PDA which accepts the L {${a^i b^j c^k}$| $i,j,k≥0$ and $i=j$ or $i=k$} I cannot quite graph how to handle the 'or' To make it easier for myself, I constructed strings where $i=...
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2answers
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For every 4 ‘c’ in the input push a ‘c’ in the stack (Push down automata)

Given the following language: L = {$a^{2m}$ $c^{4n}$ $d^{n}$ $b^{m}$ : m,n >= 0} I’m trying to design a PDA. My aproach is: -for every 2 ‘a’ push an ‘a’ -for every 4 ‘c’ push a ‘c’ -then pop them ...
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1answer
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Prove or disprove {wtw^R | |w| = |t|} is context free

The language $S_c$ defined as: $S_c = \{wtw^R \mid w,t \in \{0,1\}^\star \text{ and } \lvert w \rvert = \lvert t \rvert \}$ It looks like the language can be "pumped" by context free pumping lemma, ...
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Construct a PDA for at least one $w_i$ $\neq$ $w_{i + 1}^r$?

My assignment asks Let $S = \{ w_1\#w_2\# \dots \#w_k | k ≥ 2; (∀i ≤ k)w_i ∈ \{0, 1\}^\star ; (∃i < k) w_i\neq w_{i + 1}^r$ , i.e., not every string $w_i$ is equal to the reversal of $w_{i+1}$. ...
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1answer
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Is this a CFL: $L_1 = \{wxyx | w, x, y \in (0 + 1)^+\}$?

I recently found a question asking whether the language given below is context-free or not: $L_1 = \{wxyx | w, x, y \in (0 + 1)^+\}$ My intuition is that I can design a non-deterministic push-down ...
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1answer
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Developing a Context Free Grammar whilst knowing the number of terminals

I am trying to develop a CFG for the language $L$ defined by: $L = \{a^{n+2}bba^{n-2} | n > 1\}$ The problem I am having is that I cannot develop the CFG for this language no matter what I try. ...
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1answer
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Creating a PDA for the language L = {$a^{m}$ $b^{n}$ : m $\neq$ n}

I didn‘t find a DPDA for the language L = {$a^{m}$ $b^{n}$ : m $\neq$ n}, so I guess an NPDA is the only option. NPDA are not very intuitive to me. The only solution I found online is: I don‘t ...
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Pushdown automaton from given code for parsing a while statement

I was preparing for my exam and have some questions that can possibly come on the test. There is a task to make pushdown automata from a given code: ...
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Can there be a language not Context free but still PDA acceptable?

Let the input alphabet be $Σ = \{1,x,=\}$ Let the stack alphabet be $\tau = \{1,\$\}$ where $\$$ is the initial stack symbol. Let,$q_0$ be the initial state of the PDA,$q_f$ be the final state of PDA,...
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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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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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Understanding PDA for odd length string with middle symbol 0

I came across this pdf, which describes the language of odd length string with middle symbol 0 as follows: Doubts: I dont understand the transition labels. In standard resources like books by ...
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1answer
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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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Push Down Automatas: Is it still an accept state if stack is not empty?

I'm currently seeing if a PDA is in an accept state give an input string. After reading the entire input tape, I am currently in the accept state. However, in the stack, there are two items in it. So ...
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1answer
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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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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
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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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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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can a PDA without lamda-transition accept every context free language? [duplicate]

I want to know if every context-free-language can be constructed with a PDA without lambda transitions. I have tried to give a counter example but couldn't. Is there a theorem proving such statement ...
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Converting an NPDA to a CFG

I have a question regarding conversion of NPDA to CFG. The above picture is from my lecture slides. I dont understand why they are saying 1 can be popped while transitioning from q0 to q1. It is in ...
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Possible number of DFAs, NFAs, DPDAs, NPDAs, NDTMs and DTMs for various input parameters

I came across problem asking for possilble number of DFAs for a given number of states and alphabet. I started guessing if we can find possible number different automatas for given number of states, ...
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1answer
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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
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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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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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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
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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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