Pushdown automata are a type of automata that employ stacks. They are more capable than finite state automata but less capable than Turing machines. The term "pushdown" refers to the fact that the stack can be regarded as being "pushed down" like a tray dispenser at a cafeteria, since the operations never work on elements other than the top element. To be used with [automata].
Questions tagged [pushdown-automata]
31 questions
7
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0 answers
Unambiguous formal grammars for a specific class of languages
Suppose that $w \in \{0; 1\}^*$ is a binary word. Let's denote the number of $0$-s in $w$ as $\#_0(w)$ and the number of $1$-s in $w$ as $\#_1(w)$.
Now suppose that $q \in \mathbb{Q}$ is a positive rational number. Consider the language $L_q \subset…
Chain Markov
- 16,012
4
votes
1 answer
Finding Context Free Grammar for a language
I was trying to find the CFG for the language below. However, I couldn't do that. Can anyone help with this problem?
$$\{1^n 0^m 1^k 0^p | n \geq 2, m,k,p \geq 1, n+k = m+p\}$$
bazzinga
- 43
4
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0 answers
Is the set of pushdown transductions closed under composition?
Let’s define a pushdown transducer as a 9-tuple $V = (A, B, S, Q_A, Q_S, \phi, \psi, \chi, q_0)$, where $A$ is the finite input alphabet, $B$ is the finite output alphabet, $S$ is the finite stack alphabet, $Q_A$ are the finite set of…
Chain Markov
- 16,012
3
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0 answers
Is pushdown transduction of a periodic sequence periodic?
Let’s define a pushdown transducer as a 9-tuple $V = (A, B, S, Q_A, Q_S, \phi, \psi, \chi, q_0)$, where $A$ is the finite input alphabet, $B$ is the finite output alphabet, $S$ is the finite stack alphabet, $Q_A$ are the finite set of…
Chain Markov
- 16,012
2
votes
0 answers
This language is not context free but has a PDA?
Language is
$B = \{w \in \Sigma^* \mid w = a^n\#b^{2n}\#a^n \text{ for some } n \in \mathbb{N}\}$.
Assume the alphabet is $\Sigma = \{a, b, \#\}$.
I know this language is not context-free.
But below is a PDA that accepts all words from the above…
bhujangee
- 21
2
votes
1 answer
Transition function of non deterministic pushdown automata
I was reading book on Automata Theory by Peter Linz.
He gives transition function of the non deterministic finite automata as follows:
$\delta:Q\times (\Sigma\cup\{\lambda\})\rightarrow 2^Q$
But the transition function of non deterministic…
RajS
- 1,343
2
votes
1 answer
construct a linear pushdown automata
I am struggling with the following problem:
I received a special type of pushdown automaton, called linear pushdown automaton.
This PDA is special because once I used pop I can't use push anymore.
The formal definition…
misha312
- 537
2
votes
1 answer
Can turing machine solve halting problem on a pushdown automaton?
I meant, given a turing machine, judge whether a pushdown automaton will halt.
Pushdown automaton: a finite state machine with a stack
If so, is there any unsolvable problem weaker than halting problem?
l4m2
- 229
1
vote
2 answers
Find a Context Free Grammar (CFG) with 3p zeroes and 5q ones
How can I construct a context-free grammar for the following language?
The language is: $L = \{{(0 + 1)^* | \text{#}0 = 3p, \text{#}1 = 5q, p, q \geq 0} \}$.
I can construct a CFG for L if the zeroes and ones are grouped, such as strings of the form…
brodar
- 177
1
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0 answers
Proof of sentence "A language L is context-free if and only if L is accepted by a pushdown automaton."
I have the proof below in my lecture. I would be very grateful if someone could explain the argumentation for the case $\alpha = BC$. Furthermore, I do not fully understand the subsequent arguments for cases 2 and 3. Overall, I have been wondering…
Rico1990
- 295
1
vote
2 answers
How to generate a context free grammar for the language $a^i b^j c^k$ where $i+j>k$?
How to generate a context free grammar for the language $a^i b^j c^k$ where $i+j>k$?
My initial thought was to find the CFG for $i+j=k$, and then go from there but I've been unable to adapt it. What I have so far is:
$$S=aSc\mid…
James
- 19
1
vote
1 answer
Solution Verification: Is this language context free? (Building a pushdown automaton).
Here's the question:
Given $L_A$ and $L_B$ are two regular languages over the alphabet $\sum=\{1,2,3\}$, is the following $L$ language context free? Prove your answer.
$L = \{w\in L_A \mid \exists x\in L_B \text{ such that }|x|=2|w|\}$
I would…
Pwaol
- 2,141
1
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0 answers
Is it possible for a DPDA(deterministic pushdown automaton) to have both transitions: (q, aw, xyz) -> (q, w, yz) and (q, bw, xyz) -> (q1, bw, xyz)?
Where aw/bw are input contents & xyz/yz are stack contents.
If captioned question is yes.
Than expressed these 2 transitions by delta transition form:
delta(q, a, x) = (q, epsi)
delta(q, epsi, epsi) = (q1, epsi)
Above 2 transitions is not allowed…
Shaq Xu
- 81
1
vote
2 answers
Decidability of DCFL and Undecidability of CFL with respect to regularity
I synced with this Hendrik Jan's answer that to prove undecidability of regularity for CFL is usually obtained from two properties of the context-free languages: (1) they are closed under union, and (2) universality is undecidable.
And for DCFL…
user976798
1
vote
1 answer
Does both the language and its complement being context free imply it being deterministic context-free?
Suppose $L \subset A^*$ is context free and $A^*\setminus L$ is also context free. Does it mean, that $L$ is deterministic context free?
If it is not, I would like to see a counterexample (I failed to construct one myself).
Note that the converse is…
Chain Markov
- 16,012