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

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1answer
32 views

Determine whether a context-free language is deterministic or not

I define language $L = \{a^k a^m b^m c^k \} \cup \{a^n b^n b^k c^k\}$ and I want to determine if it's deterministic context free language or it is nondeterministic. so I tried to create pushdown ...
2
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1answer
22 views

Conversion from nondeterministic PDA to deterministic PDA

Why is the conversion from nondeterministic PDA to deterministic PDA not possible?
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2answers
66 views

How to understand pushdown automata intuitively?

What is an intuitive way of understanding what a push down automaton is capable of computing?
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1answer
98 views

Difference between DPDA and NPDA?

What are the major differences between Deterministic Push Down Automata and Non-deterministic Push Down Automata? Which one is faster and how? Also what are the drawbacks of DPDA with respect to NPDA. ...
1
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1answer
49 views

PDA for all non-palindromic strings of even length

I had a homework assignment where I had to build a PDA over the alphabet $\{a,b\}^*$, accepting $L = \{x \mid x \text{ is even but not a palindrome}\}$. I already turned it in, but I know I had it ...
1
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1answer
28 views

Removing $\epsilon$ transitions in a NPDA

NPDA's and general NFA's may not halt for finite inputs like DFA's do because of their $\epsilon$ transitions. However, NFA's with $\epsilon$ transitions could be converted to those without any ...
1
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0answers
20 views

Decidability Proof of $A_{Cfg}$

I am a beginner to complexity theory and I came up with the following proof of decidability of $A_{Cfg}$ = {$<G,w>|G$ is a context free grammar that generates string $w$} The Turing machine ...
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0answers
18 views

turing machine decidability language

I must show that this language is decidable but I think it's not {D, Ρ} | D is a DFA and P is a ΡDA which L(D) ∩ L(Ρ) = ∅ } Here what I think I give a reduction from E(TM). I suppose that this ...
1
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1answer
44 views

Why do we pop the dollar symbol when it's already present in the stack in PDA?

Could anyone tell the reason for popping the top of stack(dollar symbol) as said in this lecture(p.54) when there's already dollar symbol in the stack. I would like to know if we could replace the ...
0
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1answer
41 views

Characterizing a CFG equivalent to a special type of PDA

Consider a nondeterministic PDA $P$ which pushes/pops at most one stack symbol on a transition. Suppose that for every string $\sigma \in L(P)$, there is an accept computation of $\sigma$ in $P$ which ...
0
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1answer
34 views

Pushdown Automata: How can I recognize a ratio threshold between two symbols in a string?

I'm trying to design a pushdown automata where there are two symbols in the alphabet and the accept state is when there is >= 60% of symbol A. I'm trying to think in terms of what to save on the ...
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1answer
69 views

Converting a language to a PDA?

I am trying to convert the follow language $$L = \{0^m1^n \ | \ 0 \le m \le n \le 2m\}$$ We have an exam in 2 days and the professor didn't teach us much about PDA's. They will be on the test though ...
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1answer
9 views

Relation of deterministic push down automata and lower elementary recursion

Deterministic context free languages are the context free languages that can be accepted by a deterministic push down automata. Deterministic context free languages can be recognized by a ...
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0answers
19 views

What is the difference between Moore's algorithm and partition refinement algorithm for DFA minimization?

Both the algorithms use the partition method to minimize the DFA. I cannot understand the difference between them. Can someone give an example where we can see the difference between them.
0
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1answer
37 views

How is CFL-reachability solvable in exponential time and space?

I have read a paper which mentions that CFL-reachability is solvable in exponential time and space. Intuitively, I suppose that one need to explore through all the sub-paths in the PDA for a CFL. ...
1
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1answer
113 views

Deterministic vs. Non-Deterministic PDA?

The following is an example of language $a^nb^n$ where $n \geq 1$ From what I have heard that in finite state machines if you see epsilon moves, then it is NFA otherwise it is DFA. But in this ...
1
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1answer
87 views

Calculi for a computability class

Proving two push down automata equivalent is undecidable. But proving two finite state machines equivalent is decidable. You also cannot write a programming language that allows expressing the ...
2
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2answers
52 views

Techniques to create a PDA for a language that is the conjunction of two languages

When I was working with finite automata, I figured out that we can put together two FA two build a new one that is the intersection between the two. This is possible because regular languages are ...
0
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1answer
71 views

DPDA for $L_1 = \{0^i1^j2^k3^m | i,j,k\ge 0,m = i+j+k\}$ according to empty stack criterion

I'm having some trouble with the following language: $L_1 = \{0^i1^j2^k3^m | i,j,k\ge 0,m = i+j+k\}$ with alphabet $A=\{0,1,2,3\}$ I'd like to find a deterministic pushdown automata to recognise it ...
1
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2answers
80 views

How to convert PDA to CLF

I learned how to convert context-free grammar to pushdown automata but how can I do the opposite? to convert PDA to CFG? For example: to write CLF for the automata EDIT: My attempt: $S=A_{03}$ ...
2
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0answers
22 views

Why we don't care about minimizing Push Down Automata & Turing Machines? [duplicate]

I never heard or read about the concepts of "Minimizing Push Down Automata or Turing Machines"? why we are not concerned about minimizing them, in general?
2
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1answer
64 views

Why is this NPDA?

I am studying PDA at the moment, and I came up with this question. The figure above tells me that although both PDA accept the same language, one is non-deterministic and the other is ...
0
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0answers
15 views

PDA for recognize two same substrings in string [duplicate]

Good day, I have to devise a push-down automata for this language L={w∈{a,b}∗, w is not of the form xx for any x∈{a,b}∗} It's not necessary to write down ...
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1answer
68 views

Is a Pushdown Automata possible for this language?

PDA for a Language L = { $a^i b^j \mid i \neq 2j+1 \}$ over the Alphabet $\Sigma = \{a,b\}$ If it can be constructed, how? Edit : I've tried make the PDA for $$L = \{ a^i b^j \mid i = 2j+1 \}$$ ...
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0answers
38 views

confirmation of pushdown automata questions

I have the following questions below that I have gotten from a practice paper but have no answers for them. I have completed them but am not sure if they are right, If anyone could confirm whether ...
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1answer
77 views

How to find what language a PDA accepts?

Given the following PDA describe the language it accepts. ...
2
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0answers
78 views

What are some applications of 2 stack pushdown automata?

What are some real world application for 2 stack pushdown automata, as i can only find pushdown automata applications in the internet
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2answers
60 views

Can a deterministic language be accepted by a deterministic Push Down Automaton?

I have a question that asks me to show that the PDA of the language L is not deterministic, but that the language is nevertheless deterministic. I was under the assumption that any deterministic ...
2
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0answers
41 views

Expressing classic automata in modern terms

This semester I was introduced to finite automata (FSM), then pushdown automata (PDA), and now the Turing machine (TM). Granted that there're many possible implementations of these abstractions ...
1
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0answers
54 views

what is the CFG for a^ib^jc^k where i+2j=3k [closed]

i'm trying to find a context-free grammar that recognize the language below: $L=\{a^ib^jc^k| i+2j=3k\}$ i was trying to divide this language to three languages like this: $ i=j=k$ $ 3i=k \text{ ...
1
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0answers
31 views

Language involving length constraints and reversal

Why is the language $A=\{wtw^r: w,t\in\{0,1\}^*\text{ and }|w|=|t|\}$ not a context free language? It is turning out to be really tricky. Is there an easy way to show this?
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1answer
57 views

How to design a PDA for the language of words with s a's, t b's and s⋅t c's? [closed]

I have the language $\qquad L=\{ a^s b^t c^m \mid s,t,m \; \in \; \mathbb{N^{+}} \text{ and } t<4, s \cdot t=m\}$. How do I go about designing a PDA for it ? I can't figure out a way to deal ...
2
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2answers
192 views

Formal construction of PDA intersecting a DFA

Given the PDA $P = (Q_P,\Sigma,\Gamma_P,\delta_P,F_P)$ and the DFA $D = (Q_D, \Sigma, \delta_D,q_D,F_D)$ What is the 6-tuple definition of the PDA such that: $L(P') = L(P) \cap L(D)$ I don't ...
8
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1answer
310 views

Is non-determinism in a non-deterministic turing machine different from that of finite automata and push down automata?

Let a input string be given as $w_1w_2...w_n$. Then if a NFA is currently in state $r$ ( and has read the input upto alphabet $w_i$ ) then before reading the next input symbol the NFA splits into two ...
3
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1answer
64 views

When does a PDA split?

In case of NFA, if the NFA is in a state and reads $\epsilon$ ( empty string ) the NFA splits in to two, with one being at the current state and other with the state along the $\epsilon$ transition. ...
4
votes
1answer
80 views

How powerful is a k-stack pushdown automaton with a unary stack alphabet?

I'm interested in pushdown automata with a unary stack alphabet: let's call them UPDA's. Define a $k$-UPDA to be a pushdown automaton with $k$ stacks, each with a unary stack alphabet. I've figured ...
1
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1answer
208 views

Construct Pushdown Automaton that accepts language $x\in\{a,b\}^*, a=2b$

I've been studying Computation Theory, and in an exercise I am asked to construct a PDA that accepts the language $L=\{x\in(a,b), \#_a(x) = 2\#_b(x)\}$, where $x$ is the input string and ...
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0answers
52 views

Linear time parsing from star of context free language

I was wondering if there are cases in which the star closure of a language can make the resulting language easier to parse. In particular, if I have this grammar: ...
1
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1answer
551 views

Converting final state PDA to empty stack PDA

I'm having a problem understanding this conversion. Let's say we have a CFL like this: $ { a^nb^m : n > m } $ A final state acceptance PDA for this language would push $A$ symbols in the stack for ...
4
votes
1answer
226 views

pda: transformation between acceptance by empty stack and final states

I am stuck with understanding the transformation of final-state acceptance automaton into empty-stack acceptance automaton. From everywhere that I've read, it always says introduce a new start state ...
0
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2answers
52 views

Push down automata what to do when there is no suitable transition

This is a question that has emerged from a recent quiz I have taken. In short Consider the following transitions on a push down automaton. Assume the starting state is q. Which one of the ...
0
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0answers
12 views

Construction of NPDA with inequality check [duplicate]

I'm currently struggling to construct a nondeterministic PDA with an amount of states in $O(n)$ that accepts the following language: $L = \{wcx \, | \, w,x \in \{a,b\}^n \land w \not= x\}$ with c ...
4
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1answer
52 views

Proof that CFL aren't closed under intersection using synchronous parallel (N)PDA composition

It is well known that the class of CFLs is not closed under intersection as follows e.g. from the following example: $$L_1 \cap L_2 = \left\{ a^mb^mc^n \mid m,n \ge 1 \right\} \cap \left\{ a^mb^nc^n ...
2
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0answers
40 views

NPDA, guessing capability and stack as an exclusive resource

Context Free languages is exactly the class of languages recognized by Nondeterministic Push Down Automata (NPDA). We can view a nondeterministic transition as a guess; for example if $L = \{x x^R ...
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1answer
136 views

Context free grammar $\{a^n b^m c^k\; : \;k>m \; \; k>n\}$

Is this a CFL? $$\{a^n b^m c^k\; : \;k>m \; \; k>n\}$$ When on seeing $a$'s and $b$'s I push them onto stack and as I see $ c$ as input if $ TOS$ is $b$ ,I pop them ,again if $TOS$ is a,I pop ...
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0answers
12 views

Determine whether the following languages are context free [duplicate]

$L$ is context free and $L_r$ is regular and $A$ is an alphabet. The languages are: $$ L_1 = \{ uv ; u \in L , v \in L^R , |u| = |v| \} $$ $$ L_2 = \{ uxv ; uv \in L_r , x \in A, |u| = |v| \} $$ ...
1
vote
1answer
41 views

When to pump up and down?

When I'm solving a question I usually spent too much time testing whether I should pump or down? Is there any formula to know when to use which? Also, on proofing non context free grammar we use ...
1
vote
2answers
249 views

Find a pushdown automaton for { x#y ∣ x ≠ y }

I was told to built a PDA that recognizes the following language: $$L = \{x\#y \mid x,y \in \{0,1\}^{\ast} \wedge x \neq y\}$$ My attempt is basically to push $x$ to the stack for every $1$ and $0$ ...
2
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1answer
87 views

How to create this pushdown transducer? (formal languages and automata)

Create a pushdown transducer that translates $a^m b^{2m}c^{m+n}$ into $b^{n-m}$, with $n\geq m \geq 0$. How should I use the stack to remember or to compute how many characters of c to read? And how ...
2
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1answer
195 views

How exactly does a two stack pushdown automaton work?

I have to explain how a 2-PDA works and then write a program (in Delphi) which simulates a 2-PDA step by step for the language $L = \{w\$w\ |\ w ∈ \{0,1\}^n\ with\ n>0\}$. So far, so good. Now I ...