state machines with stacks, capable of accepting the set of context-free languages.

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What additional expressivity does polyvariance give in pushdown CFA?

I'm reading through Pushdown Control-Flow Analysis of Higher-Order Programs, which presents a synthesis of the Abstracting Abstract Machines technique and pushdown automata to get static analysis ...
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0answers
25 views

Constructing pushdown automata [on hold]

How do you construct a pushdown automata for this particular language.
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1answer
216 views

Is it decidable whether a pushdown automata recognizes a given regular language?

The problem whether two pushdown automata recognize the same language is undecidable. The problem whether a pushdown automata recognizes the empty language is decidable, hence it is also decidable ...
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23 views

When do we need to change the state of a push down automata?

I'm new to the subject of automata theory. I get most of the stuff, but I cannot figure out when to change the state of the machine, and when to keep the state unchanged for a particular transition ...
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15 views

Are deterministic context-free languages closed under reversal of languages? [duplicate]

It is well known that context-free languages are closed under the reversal of $L$. My answer to the question "Is the time reversal symmetry of non-deterministic computations important?" notices that ...
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0answers
23 views

Is $\{u\#v \mid u\not=v\}$ context-free? [duplicate]

Is the following language context-free? $$ \{u\#v\in\Sigma^* \mid u\not=v \text{ and } u,v\in\{0,1\}^*\} $$ You can assume $\{0,1,\#\}\subseteq\Sigma$. Unnecessary background information: I am ...
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1answer
98 views

Why is $\{a^n b^m c^p: n\neq m\} \cup \{a^n b^m c^p: m\neq p\}$ an inherently ambiguous language?

I came across a very hard interview question in last month’s Ph.D. entrance exam. It was asking which one of the languages is inherently ambiguous. Short answer says 2). Why is the language in 2) an ...
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1answer
39 views

Construction of a counter automaton for the complement of the palindromes

How would I go about constructing a nondeterministic 1-counter automaton for the language $L$ that is the complement of the palindromes $\overline{L}=\{ww^{rev}\}$ over a 2 symbol alphabet $\Sigma = ...
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1answer
147 views

PDA with N-Stacks comparison with Turing Machines [duplicate]

Is it possible to compare PDA having N-Stacks with Turning Machines. Are they equally powerful in this situation? It's been told that PDA with 2-Stacks is equally powerful to Turning Machine. But ...
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1answer
43 views

Is a k counter automata a special kind of PDA?

I understand that a 1 counter automata is a special kind of PDA where the stack alphabet consists of one symbol (ignoring the fixed bottom symbol) but what about 2 counter automata? Is it a special ...
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38 views

Simple question: Pushdown automata transition

I am currently constructing pushdown automata. can I push/pop alphabet more than two in a transition?? For example, $\delta$(a, a/aaa) means, in the state of input alphabet 'a' and stack point 'a' ...
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17 views

non-regular context free language with logarithmic stack usage [duplicate]

Can you suggest a context-free language $L$, which is: non-regular has a PDA which accepts all $w\in L$ and uses maximum stack space of $\log(|w|)$.
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1answer
59 views

Can we build a nondeterministic decider PDA using two PDAs accepting a language and its complement?

When talking about turing machines, it can be easily shown that starting from two machines accepting $L$ and its complement $L^c$, one can build a machine which can fully decide if a word is inside ...
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2answers
196 views

Which class of languages is accepted by PDA when we restrict the stack to logarithmic size?

Let $\mathrm{LOG}_{\mathrm{CF}}$ be the class of all languages recognized by a Pushdown-automaton that uses $\leq \log n$ cells of its stack for each input of length $n$. Obviously, this class is a ...
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5answers
141 views

is it possible to minimize pushdown automata?

is it possible to minimize pushdown automata? If no, why? Is it because for minimization the equivalence classes need to have a finite index and we cannot guarantee that for CFG?
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1answer
57 views

Create cfg and npda/pda for Language {ww}

I've been trying to make a CFG, and npda/pda for this language (to construct an npda for accepting the language): L(M)={ww:w∈{a,b}∗,|w| is even}. i had already solved the reverse of the language ...
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1answer
61 views

Create CFG and pushdown automaton for {ww} [duplicate]

I've been trying to make a CFG, a pushdown automaton and a regular expression for the language $\qquad L(M) = \{ww : w \in \{a, b\}^*, |w| \text{ is even}\}$. I understand how the reverse of the ...
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2answers
111 views

Pushdown Automata: CFG to PDA

I have the following grammar for a context-free language: $G = (\{S,A,B\}, \{x,y,z\}, P, S)$ with $P = \{S \rightarrow A, A \rightarrow xAz, A \rightarrow xBz, B \rightarrow y\}$ My question is: How ...
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1answer
25 views

Why is it that the transition function for DPDA's only works for 1 alphabet symbol, and 1 stack symbol?

Why is it that the transition function for DPDA's only works for 1 alphabet symbol, and 1 stack symbol? Say f is the transition function, why does having ...
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2answers
46 views

what is the best way to approach the construction of nondeterministic PDA's?

I'm trying to construct a PDA for $L = \{w0^i1^j \mid w\text{ ends in } 01 \wedge 2i=3j\}$. My understanding is that I have to first accept an arbitrary number of zeros and ones and then ...
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1answer
97 views

Language of binary strings divisible by 7

There was a question something like, "Consider the language of all integers converted to binary form. The language of all strings divisible by 7 is : 1) Recognizable by a finite-automaton. 2) ...
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2answers
121 views

PDA recognising all strings with a $1$ in the second half

My professor gave us an old exam to look over for our final exam and I am having a hard time understanding the push down automata problem he gave. In the problem it says: Let $\Sigma = \{0,1\}$ ...
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2answers
60 views

Is it possible to write an HTML compiler with no mutable state?

That's probably a vague question but allow me to try and give an example: My compiler does transformations on HTML (from HTML to HTML). It scans a flattened DOM tree, and relies on lookbehinds (on ...
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1answer
62 views

PDA - Sum of Two Characters = Sum of Two Other Characters

For one problem I have to solve, I'm given a Language: L = {a^r b^s c^t d^u | r+s = t+u} And from it told to construct a PDA that accepts it. I can construct a ...
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1answer
62 views

Simple Pushdown Automaton

I'm currently learning about PDAs and their power when constructing them from Context-Free Grammars, however I'm still unsure of how to properly construct a CFG, and then a PDA from that CFG. In the ...
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0answers
18 views

Simulate NPDAs with DTMs using only polynomial overhead

We know by polynomial-time parsing algorithms like the classical CYK algorithm that $\mathrm{CFL} \subseteq \mathrm{P}$. Furthermore, it is easy to show by direct simulation that $\mathrm{DCFL} ...
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1answer
49 views

Can a DPDA be created for a Language which includes the null string?

Can a DPDA be created for a Language which includes the null string? The way I understand it, in a DPDA, you can have at most 1 move from any instantaneous description Delta(q,a,Z) where q is a ...
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2answers
56 views

What is the purpose of ϵ-transitions in PDA?

$A = \{a^i b^j c^k\mid i = j\text{ or } j = k; i, j, k \ge 0\}$. In its push down automaton should not there be the red colored transition instead of the black colored one?
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1answer
39 views

Is “duplicate” in RPN enough for replacing variable binding in term expressions?

I try to work out some consequences of storing (or "communicating"/"transmitting") a rational number by a term expression using the following operators: $0$, $\mathsf{inc}$, $\mathsf{add}$, ...
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1answer
65 views

Intersections of some context-free languages

Suppose We have Some language as follows: $L_1=\{w^* | w=x \text{ and } x \in \Sigma^*\}$ $L_2=\{ww^R ww^R | w \in ( \Sigma + \Sigma)^*\}$ $L_3=\{w | w=xy, x,y \in \Sigma^*, y \text{ is a ...
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1answer
325 views

Are DCFLs closed under reversal?

According to this chart, DCFLs are closed under reversal. However, I am not convinced as the intuitive proof (reversing the arrows of the controlling finite state machine and switching the pushes and ...
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1answer
130 views

Pushdown Automata Challenge

I read one old-midterm exam on Automata. consider: the language that accepted by above pushdown automata is not generated by which of the following grammar? 1) S->aBaa|a$\epsilon$ ...
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1answer
37 views

Do NFAs with ϵ-transitions accept languages that no PDA can?

Is it correct to say that there are languages that a NFA with epsilon recognizes but a PDA is not? I think that it is wrong but I cannot find a suitable explanation.
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1answer
132 views

Non Deterministic PDA accepted language not clear

This is a PDA from the lecture slides I'm using: They say it accepts all words that contain double a's. While it makes some sense it's not full proof. What prevents the second a to be read in the ...
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2answers
58 views

Incorporating newline-as-statement-terminator heuristics into context-free languages

Several block structured languages (Scala, Go, Ruby, Julia, Quorum, ...) use semicolons as statement terminators, but allow newlines instead of semicolons under certain circumstances. My question is: ...
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1answer
51 views

Is there a PDA for every Type 3 Grammar?

we learned that for every type 2 grammar G exists a PDA A with L(A) = L(G). But does for every type 3 grammar G exist a PDA A_G with L(A_G) = L(G)? I think it does, because type 2 grammar is a subset ...
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15 views

How would i design a PDA that accepts order of sentence? [duplicate]

How would i design a PDA that accepts order of sentence. In Natural Language Processing, context free grammars are used to identify valid English sentences from invalid once. For instance, ‘Lorem ...
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1answer
72 views

writing a Context free grammar for a language [closed]

Hi I have two question about this language: L = {a^i b^j c^k | i = 2*j OR j=2*k } 1)Finding a CFG 2)If in condition part we put AND instead of OR , is this language remains CONTEXT FREE or not ?? ...
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142 views

Good introductions to Formal Language Theory and Formal Grammars

Does anyone know any good introductions to Formal Language theory and Formal Grammar, that cover the mathematical basis of Syntax and things like context free grammars and pushdown automata. In ...
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1answer
111 views

Computing the intersection of two NPDA where it is possible

Apropois to Raphael's suggestion on Intersection of two NPDAs: Let $A_1$ and $A_2$ NPDA for context-free languages $L_1$ and $L_2$, respectively. Assuming that we know that $L = L_1 \cap L_2$ is ...
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2answers
65 views

Intersection of two NPDAs

Is there a way to take the interection of two NPDAs? I can't seem to find anything that can make that happen, but it seems like the type of thing that is should be relatively trival.
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2answers
214 views

How many states when converting CFG to PDA

When converting a CFG to a PDA I know that you get three main states, Qstart, Qloop and Qaccept. But Qloops will need a various amount of states, and my question is how many? Is there a way to find ...
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1answer
63 views

Proving a language is not a regular language but a context free language [duplicate]

I have the languages $L_1$ and $L_2$ such that $L_1 = \{a^nba^n :n \in N\}$ and $L_2 =\{a,b\}^*\setminus L_1$. I want to prove that $L_2$ is not a regular language. I know that to prove that $L_2$ is ...
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1answer
117 views

Why Deterministic PDA accepts $\epsilon$ input but DFA not

I was going through a deterministic PDA that accepts $wcw^R$ (described in Ullman's textbook), in which the last transition is given as $(q_1,\epsilon, Z_0)\to(q_2,Z_0)$, where $q_2$ is the final ...
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1answer
77 views

A NPDA for the language $L = \{w \mid w \in \{a,b,c\}^*, n_c(w) = n_a(w) + n_b(w)\}$

Consider the language $L = \{w, w \in \{a,b,c\}^*, n_c(w) = n_a(w) + n_b(w)\}$, where $n_q(\omega)$ is defined to be "the number of $p \in \omega$. I have tried a couple of PDA's that follow this ...
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2answers
136 views

Why are pushdown automata countable? [closed]

I began a chapter in a textbook on computational theory where they begin to talk about decidable languages. The problems in this section are pretty confusing and I honestly don't know how to begin ...
2
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1answer
319 views

Creating a Deterministic Push Down Automata

I saw this old post on stack overflow of a PDA that accepts a language where there are exactly twice as many a's as there are b's. The image they used is below and so is the link to the post itself. ...
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0answers
46 views

Are all PDA equivalent to two-state-PDA? [closed]

We know algorithm to convert each PDA in the underlying grammar that generates the language the PDA recognize. But we have also the algorithm for creating a two state pda from a grammar. This ...
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1answer
139 views

How to find a Deterministic PDA for an intersection of languages

There are two languages, $\qquad L_1 = \{w\in\{a,b\}^*: N_a\leq N_b\}$ and $\qquad L_2=\{w\in\{a,b\}^*: N_b\leq 2N_a\}$ where $N_a$ means the number of occurrences of $a$ in the string $w$. Same ...
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2answers
236 views

How to get 2-state PDA for CFG?

I'm studying for my Computing languages test and there's one idea I'm having problems wrapping my head around, as far as I know for any Context Free Grammar (CFG), we can design a 2-state Pushdown ...