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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How can one simulate a PDA with a FIFO queue PDA?

I'm trying to figure out how a pushdown automata (PDA), which we know uses a stack (LIFO) can be simulated by a queue (FIFO). I understand that in a regular PDA, we only have access to the top most ...
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2answers
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CFG and PDA for the grammar that has perfectly nested parentheses and brackets

I gotta make a CFG and PDA for the grammar that has perfectly nested parentheses and brackets. $\qquad\begin{align} S &\to [S] \\ S &\to (S) \\ S &\to SS \\ S &\to \varepsilon \...
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2answers
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How do I show that whether a PDA accepts some string $\{ w!w \mid w \in \{ 0, 1 \}^*\}$ is undecidable?

How do I show that the problem of deciding whether a PDA accepts some string of the form $\{ w!w \mid w \in \{ 0, 1 \}^*\}$ is undecidable? I have tried to reduce this problem to another undecidable ...
3
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3answers
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Constructing deterministic PDA for not regular language

Let the input alphabet be $\Sigma = \{a,b,c\}$ and L be the language of all words in which all of the a’s come before all of the b’s and there are the same number of a’s as b's and arbitrarily many c’...
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2answers
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When generating a PDA from a CFG do I have a receiving state?

Thw Wikipedia article on Pushdown automata doesn't explain what the receiving state is for the generated PDA it just states that there is but one state.
50
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2answers
38k views

Is a push-down automaton with two stacks equivalent to a turing machine?

In this answer it is mentioned A regular language can be recognized by a finite automaton. A context-free language requires a stack, and a context sensitive language requires two stacks (which is ...
3
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1answer
5k views

Context-free grammar to a pushdown automaton

I'm trying to convert a context free grammar to a pushdown automaton (PDA); I'm not sure how I'm gonna get an answer or show you my progress as it's a diagram... Anyway this is the last problem I have ...
2
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1answer
1k views

Eliminating useless productions resulting from PDA to CFG converison

In my class we used a Pushdown Automata to Context Free Grammar conversion algorithm that produces a lot extraneous states. For example, for two transitions, I am getting the following productions ...
10
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1answer
811 views

How to prove that ε-loops are not necessary in PDAs?

In the context of our investigation of heap automata, I would like to prove that a particular variant can not accept non-context-sensitive languages. As we have no equivalent grammar model, I need a ...
23
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1answer
3k views

Decide whether a context-free languages can be accepted by a deterministic pushdown automaton

Given a context-free grammar G, there exists a Nondeterministic Pushdown Automaton N that accepts exactly the language G accepts. (and visa versa) There may also exist a Deterministic Pushdown ...
14
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2answers
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Does the language of Regular Expressions need a push down automata to parse it?

I want to convert a user entered regular expression into an NFA so that I can then run the NFA against a string for matching purposes. What is the minimum machine that can be used to parse regular ...
10
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3answers
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If $L$ is context-free and $R$ is regular, then $L / R$ is context-free?

I'm am stuck solving the next exercise: Argue that if $L$ is context-free and $R$ is regular, then $L / R = \{ w \mid \exists x \in R \;\text{s.t}\; wx \in L\} $ (i.e. the right quotient) is context-...
4
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1answer
4k views

How does a two-way pushdown automaton work?

Note that by "two-way pushdown automaton", I mean a pushdown automaton that can move its reading head both ways on the input tape. I recently had the question of determining the computational power ...
5
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6answers
22k views

Are Turing machines more powerful than pushdown automata?

I've came up with a result while reading some automata books, that Turing machines appear to be more powerful than pushdown automata. Since the tape of a Turing machine can always be made to behave ...
39
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2answers
6k views

Are there inherently ambiguous and deterministic context-free languages?

Let us call a context-free language deterministic if and only if it can be accepted by a deterministic push-down automaton, and nondeterministic otherwise. Let us call a context-free language ...
7
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1answer
757 views

Converting a context free grammar to a PDA -- is my solution correct?

I'm reviewing for my midterm and wanted to post this to see if anyone can spot any errors. Im supposed to make a PDA that recognizes this CFG: $\qquad\begin{align} S &\to R1R1R1 \\ R &\to ...

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