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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PDA equivalent to an $\varepsilon$-free PDA

Say that a PDA is $\varepsilon$-free if it contains no $\varepsilon$ transitions (that is to say, $\varepsilon$ is not in the recognized string symbols even if it still is a stack symbol), but it may ...
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Hardwiring input in DFAs and PDAs

A Turing Machine can be converted into a Turing Machine that has a specific input coded into it's description. This Turing Machine can then be run on empty input. Can we do the same for PDAs or DFAs? ...
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Is there a one-state PDA that recognizes every context free language?

Here, I read this: For all CFL, there is a one-state PDA that recognizes this language. What is the proof/idea behind this claim? CFL: Context Free Languages PDA: Push Down Automaton
whoisit's user avatar
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Create PDA from grammar

I am trying to construct a PDA for the following grammar: I use jflap but am not sure how to proceed when making PDA compared to DFA which were way easier. Can anyone please point me in the right ...
completenewb's user avatar
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Not understanding example of a Pushdown Automata

The first example of a (nondeterministic) pushdown automata given in Linz' An Introduction to Formal Languages and Automata is the following: Example 7.2: consider $Q = \{q_0,q_1,q_2,q_3\}$, $\Sigma =...
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infinite loop in PDA

let L be defined as $L = \{0^{2k} | k \in \mathbb{N}\} \subset \{0,1\}^*$. language L can be described by a nondeterministic pushdown automaton P such that there exists at least one input for which P ...
Jacob Martina's user avatar
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Length of an $\varepsilon$-computation in complete DPDA

I consider a deterministic pushdown automaton. Given that there are some differences between definitions, here is mine: the syntax is given $A = (Q, \Sigma, \Gamma, \Delta, q_0, Z_0, F)$, with $q_0\...
Nathaniel's user avatar
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Is the Given Languages CFL or DCFL?

$L_1$ = {$a^nb^mc^xd^y$|$n=m$ or $x=y$} $L_2$ = {$a^nb^xc^md^y$|$n=m$ or $x=y$} For $L_1$: Push a's Now pop the same number of b's , Given n=m If Stack is empty and x=y=0 accept the Langauge else ...
Vedant Khandelwal's user avatar
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Is this correct Context free grammar(CFG) for these two languages?

Question 1: L = { 0^n 1^n | n > 0 } My answer = S -> 0 S 1 | 10 Question 2: L = { 101^n0^2n | n > 0 } My answer = S -> 101 S 00 | 100 Can anyone correct this if there is any issue with ...
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Two Counter word count language Nondeterministic Pushdown Automata (NPDA) problem actually Context Sensitive unless counters are multiples

Classic text (Linz, P., & Rodger, S. H. (2022). An introduction to formal languages and automata. Jones & Bartlett Learning.) describes the following language where one is to describe an ...
John Daniels's user avatar
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Two Counter word count language npda' problem actually Context Sensitive unless counters are multiples [duplicate]

Classic text (Linz, P., & Rodger, S. H. (2022). An introduction to formal languages and automata. Jones & Bartlett Learning.) describes the following language where one is to describe an ...
John Daniels's user avatar
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Two Counter word count language npda' problem actually Context Sensitive unless counters are multiples [duplicate]

Classic text (Linz, P., & Rodger, S. H. (2022). An introduction to formal languages and automata. Jones & Bartlett Learning.) describes the following language where one is to describe an ...
John Daniels's user avatar
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CFGs and Pushdown Automata

Is this the CFG for part (a), S -> AxxyxxA A -> Ax|ε If this is the answer then this grammar would accept &...
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1 way 2 stack and 2 way 2 stack Pushdown Accepters that accepts $L=\{a^{(n^2)} \mid n \geq 1\}$

Using a 1 way 2 stack, and a 2 way 2 stack PDA, I want to check if the length of an input string is strictly a perfect square number. How can I do this in both approaches?
user164486's user avatar
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Are 2 independent PDAs equivalent to a turing machine?

I was thinking about the language $a^nb^nc^n$, which is obviously not context free, but if we run it through 2 automata at the same time (the first for $a$ and $b$ and the second for $b$ and $c$ and ...
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DPDA for language $L=\{a,b\}^* \setminus a^nb^n \setminus b^na^n$

How to construct DPDA for the following language $L=\{a,b\}^* \setminus a^nb^n \setminus b^na^n $ $L_1 = \{a,b\}^* \setminus a^nb^n =\{a^i b^j \, | \, i>j\}\,\cup\,\{a^i b^j\ \ | \ i<j\}\,\cup\...
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Show that the language $L=\{w|w$ has odd length and the middle symbol is a $0\}$ is Context-Free and construct a PDA that accepts it

Were w is any string composed over the alphabet $\Sigma = \{0,1\}$. For the first part of the exercise I've tried decomposing the problem into three different ones, mainly the first one is for the ...
Lorenzo's user avatar
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Constructing an equivalent Pushdown Automaton

I'm working on an exercise (not relevant for evaluation) that involves constructing an equivalent nondeterministic stack machine from a given machine with epsilon-transitions. However, I'm having ...
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can a DPDA have two transition to different states when you pop a different symbol?

I have a question about the DPDA. Is it possibly to have two transitions that read the same input but do different in the stack? An example would be A transition from q1 to q2 where I read input ( pop ...
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can you read and push different symbols in a DPDA?

I have an easy question about the DPDA. Could you read an input and push a different symbol to the stack. An example would be A transition from q1 to q2 where read input is v pop is epsilon(empty ...
ee ss's user avatar
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Deterministic pushdown automata that checks for a specific variable in nesting levels

I want to define a DPDA based on a set of rules: one or more uppercase letters ('A'-'Z') is a formula. one or more lowercase letters ('a'-'z') is a formula. if X and Y are formulas, then this is a ...
phuck's user avatar
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Can a pushdown automaton write more than one symbols on to stack on one reading from from input tape?

The formal definition of the pushdown automata according to Mike Sisper's book on theory of computation is as follows: . The transition function however only takes in one symbol from the stack (after ...
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Equivalent context free grammar for every pushdown automaton?

Equivalent context free grammar for pushdown automata [edit] This machine does not accept L = {a^(n)b^(n)c^(n) | n > 0} and instead accepts L = {a^(2n+1)b^(2n+1)c^(2n+1)}; also, as a side note ...
Hiefenhoomer's user avatar
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Simple pushdown automata question

I'm trying to derive the language it represents. However, I'm kind of new to those topics. What happens if input b is gathered once or more than one time at state q without a in the stack? It does not ...
mark's user avatar
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Constructing a PDA for $L=${$\exists i,k\in \mathbb{N} : |w|=2k, w_i \neq w_{k+i}$}

I have the main idea, yet I'm uncertain on how to construct this PDA (in terms of states, transitions) We can assume the alphabet $\Sigma$ is {$0,1$}, proving for $\Sigma=${$0,1$} is a sufficient ...
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How PDA decide when and which state to transform to?

[1] gives an example for PDA which contains rules of: (p,e,Z,q,Z) (p,e,A,q,A) and says, The third and fourth instructions say that, at any moment the automaton ...
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Mike Sipser and Wikipedia seem to disagree on Chomsky's normal form

Here's what Wiki says: And here's what Mike Sipser says in his Introduction to Theory of Computation: The problem arises when you try to read the two definitions - Mike Sipser seems to be suggesting ...
Sbeve's user avatar
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The book says 27 terminals but I only see 10. Where are they?

On page 103 of Mike Sisper's Introdution to Theory of Computation, it says that the grammar has 27 terminals (26 being the letters of the English Alphabet and 1 being the space character) but in the ...
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Need to create CFG that requires sum of other letters

I have a homework assignment that requires me to create CFG $G$ for $$L = \{a^i b^{i+j+k} c^j d^k\}$$ so that it can accept words like ab, aaabbbbd, abbbcd, but it should not accept abba, aabbbbbc, or ...
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Pushdown Automata Construction

I had an assignment in which I had to design a pushdown automata that recognizes the language ${w \in [a,b,c]^*|w }$ have the same number of "ab" and "ba". Tried to make a pushdown ...
Jack Vork's user avatar
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Is the following language recognizable by a visibly pushdown automaton?

Consider the alphabet $\Sigma = \Sigma_c \cup \Sigma_i \cup \Sigma_r$ separated into call, internal, and return letters. Assume that $c \in \Sigma_c, r \in \Sigma_c$, and $a \in \Sigma_i$. I have a ...
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prove that Every DPDA has an equivalent DPDA that always reads the entire input string

I am reading Michael Sipser's book Introduction to the Theory of Computation and in the section 2.4(chapter 2 and DCFLs section) there is a proof for the lemma that says "Every DPDA has an ...
emdhdr's user avatar
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PDA for equal number of as and b's where n>=1

How to design Push Down Automata for a language that has equal number of a's and b's where $n \ge 1$? I got how to do it for $n \ge 0$, not able to get it for $n \ge 1$.
user avatar
3 votes
2 answers
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Implementation details of "transitions" of Non-deterministic push-down automata

I am reading "Introduction to the Theory of Computation" 3rd edition ~ by Michael Sipser, page 113-114 - topic: "Context free languages, push down automata" He states that the ...
Pratik Hadawale's user avatar
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PushDown automata for a^(n) b^(2n) c^(2n) d^(n)

i got this question in a theory of computation quiz "give pda for a^(n) b^(2n) c^(2n) d^(n)" i am arguing that there is no pda for that question but our ta says that we can push 5x to the ...
ambiguous student's user avatar
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What characteristics would a PDA $A$ where $L(A)=\Sigma^*$ have?

I understand that the problem of whether a PDA accepts all strings is undecidable. However that doesn't mean such PDAs exist. To start, I'm working under the assumption that a PDA must read it's ...
Gabe Kelly's user avatar
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Intersection of CFL and DCFL

Is CFL $\cap$ DCFL = CFL, always true? CFL - Any Context Free Language DCFL - Any Deterministic Context Free Language
Chaitanya Kale's user avatar
1 vote
1 answer
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Shuffle of a DCFL and a regular language

This is problem 88 from Miscellaneous exercises of Kozen's "Automata and Computability". The shuffle $A||B$ of two languages $A$ and $B$ is defined as $\{w \mid w = a_1b_1\ldots a_kb_k,$ ...
ayan's user avatar
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Push Down Automata

I am learning about context free languages. I understand how $\{a^nb^nc^n|n>0\}$ can be shown to be not context free using the pumping lemma for CFL's. Intuitively however it seems that a pushdown ...
Manan's user avatar
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1 answer
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Understanding this PDA for non-palindromes over {0,1}

I found this PDA online that accepts all non-palindromes over {0,1}. However, I can't seem to understand how it would accept, say "01011", and not accept "101101". Can someone help ...
stylusss's user avatar
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1 answer
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Context Free Language Twist [duplicate]

I am trying to recognize a particular language, L= {a^n b^k | n<=k<=2n} and according to me it should not be CFL, as i can see two comparision i.e. firstly number of a is compare to keep count ...
Niraj Jain's user avatar
2 votes
0 answers
119 views

Minimizing DPDA

Is there an efficient algorithm for minimizing a deterministic PDA in terms of states? Is it even computable? I know that it is not possible to minimize a PDA in general, but my question is about ...
Peter Lenkefi's user avatar
2 votes
2 answers
276 views

Intuition for Sipser's proof of PDA to CFG

I understood Sipser's proof of CFG to PDA but I am having a hard time understanding his proof of conversion from PDA to CFG while demonstrating the equivalence between the two. He splits the proof (...
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Non-deterministic Pushdown Automaton to Context-Free Grammar

While doing the exercise about questions about transforming NPDA to CFG, I encountered the following question: Find a CFG for the following NPDA $M = (\{q_0, q_1\}, \{a, b\}, \{A, z\}, \delta, q_0, z, ...
Uduru's user avatar
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1 answer
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Prove that the "6-rule" CFG for arithmetic expressions below is unambiguous

Question: Prove that the 6-rule CFG for arithmetic expressions below is unambiguous. The CFG is as follows. $G = (V:=\{E,T,F\}, \Sigma:=\{+, \times,(,),x\},R,E\})$ where $R$ consists of 6 rules: $E\...
Clair Goodman's user avatar
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3 answers
148 views

Is Turing completeness necessary?

Most programming languages are Turing complete (finite memory blah blah blah), and when we design languages this is a goal. But is it really necessary? What algorithms do we typically use that require ...
StackMachine's user avatar
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2 answers
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Is this a context free language? I need to make PDA but I don't think it is doable

I got a question: Design a pushdown automata that can recognize strings in L= {$ a^n b^{2n} c^{3n} | n ≥ 0 $} . I tried to think and design it, but I couldn't find it. The best that I can think of is ...
Dwi's user avatar
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1 vote
3 answers
442 views

How to prove the language of words $a^ib^jc^k$ where $\min(i,j)\le k\le\max(i,j)$ is not context-free?

I want to prove that $\mathcal M =\{a^ib^jc^k \mid \min(i,j)\le k\le\max(i,j)\}$ is not a CFL. Using the pumping lemma, let $p$ be the constant, then I choose $w=a^pb^pc^p$. When I separate to cases, ...
Math4me's user avatar
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2 votes
2 answers
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in 2DPDA and 3DPDA:2 and 3 is the number of tapes or of stacks?

I'm struggling with the definitions of the push-down automata. In 2-DPDA and 3-DPDA, what do the numbers 2 and 3 stand for: for the number of stacks or of read-only tapes (and hence RO heads) ? ...
user18624013's user avatar
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1 answer
505 views

Possible PDA for $ L = \{ a^{3n}b^{2n} | n \ge 0 \}$ without transforming CFG to PDA

To those of you who saw my post from an hour ago - I deleted it because I came up with an idea. To summarize, I have to design a PDA for this language, without using the usual method of firstly ...
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