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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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a^nb^nc^nd^n using 2-stack PDA

I need to construct a PDA using 2 stacks for accepting the language $L = \{a^nb^nc^nd^n | $ $n \geq 0\}$. Pushing $a$'s to first stack and $b$'s to second and poping them for corresponding $c$'s and ...
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1answer
51 views

Pushdown Automata for words x#y where x and y are different words over {0,1} that share one similarity

I was instructed to create a pushdown automaton described in the title. Basically, the pushdown automaton accepts strings of the form $x\#y$ where $x$ and $y$ are strings of 1s and 0s such that there ...
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kPDA handling multiple epsilon transtions

I'm assigned to build a kPDA with 2 stacks that handles {w#w, where w is a string of (0,1)*}. I understand the # delineates the two strings, but I'm unsure of the logic when popping off stacks with ...
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Proving the Complement of a DCFL is DCFL [duplicate]

If I Have a DCFL $L$ ( a CFL which can be recognised by a DPDA ), How do I prove that $\overline{L}$ is also a DCFL I checked my textbook for a proof but I wasn't able to understand the language. Can ...
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24 views

Automaton without stack for visibly pushdown languages

This paper here describes an alternating automaton which can recognize visibly pushdown langauges without using a stack. Unfortunately the transformation from NVPA to such an automaton is skipped in ...
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1answer
19 views

Behavior of specific PDA for a certain input

Suppose we're given the non-deterministic PDA shown below which reads from the alphabet $\sum = \lbrace a,b \rbrace$. How will this PDA behave if we pass it the string $ba$? We read $b$ first and push ...
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37 views

How can I find a language from a given PDA

I have the following PDA: And a given solution for his languages ${L}_{\mathrm{End}}(M_2)$ and ${L}_{\mathrm{PDA}}(M_2)$ with $ \mathrm{L}_{\mathrm{End}}\left(\mathrm{M}_{2}\right)=\left\{\mathrm{a}^{...
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1answer
39 views

Make a Pushdown automata that accepts a language defined by strings that contain the same number of a and b [duplicate]

How do I build a pushdown automata that accepts the language over the alphabet $\Sigma = \{a, b\}$, defined by the strings $w$, such that $|w|_a = |w|_b$? I'm sorry I can't give any approach of what ...
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1answer
53 views

How construct PDA to $L = \{x \in(a,b,c,d)^* \mid -10 \leq ( |x|_a + |x|_b) - ( |x|_c + |x|_d) \leq 10 \}$

$L = \{x \in(a,b,c,d)^* \mid -10 \leq ( |x|_a + |x|_b) - ( |x|_c + |x|_d) \leq 10 \}$ I don't have any idea. Can someone help me.
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Prove $ L = \{ww^{R} \in \{a, b\}^{*} : |w|_{a} \equiv |w|_{b} \equiv 0$ $ (mod$ $13) \} $ is regular or context-free or neither

$ L = \{ww^{R} \in \{a, b\}^{*} : |w|_{a} \equiv |w|_{b} \equiv 0$ $ (mod$ $13) \} $ Exercises: If the language L is regular (build a DFA or regular expression) else if the language L is context-...
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1answer
21 views

NPDA transitions to different states by taking same input and popping same top element of a stack

Suppose i have some NPDA and there is some transition functions defined as: $\delta(q_{1},a,A) = (q_{2}, A)$ $\delta(q_{1},a,A) = (q_{3}, Z)$ Is it allowed? I understand, that since the NPDA is ...
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657 views

Turing machine VS Push Down Automaton in CFL

I want to ask that between turing machine and pushdown automaton: which abstract machine can handle context-free language (CFL) in a more efficient way, and why? I know that a pushdown automaton can ...
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1answer
58 views

Allowing an empty (epsilon) transition in a PDA

I'm trying to allow an empty transition in a PDA for the following language: Alphabet: $Σ = \{a, b, c\}$ Language: $L = \{ a^ib^j \mid i \neq j \} \cdot \{ c \}^\ast$ Examples of words in $L$: $\...
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1answer
44 views

PDA for the language of strings containing the same number of a and b

Need idea for solving the following pushdown automata: $\mathcal{L}=\{w\in\sum ^* | \#a(w)=\#b(w),|w|\geqslant 0\} \,\,\,\, \sum=\{a,b\}$ In the beginning I thought to PUSH A for input a, and then ...
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1answer
109 views

Constructing a PDA with an unequal number of a/b

I'm looking at this pdf for problems: http://www.public.asu.edu/~ccolbou/src/355hw5solf10.pdf I found question 3g to construct a pushdown automata for the following: {$ {a^i b^j}$ | ${i \neq j}$} ...
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1answer
39 views

How to prove that if $L, G$ are regular languages then $\{w\in L|\exists x\in G: |x|=2\cdot |w|\}$ is a context-free language?

Prove that if $L, G$ are regular languages over $\{a,b,c\}$ then $H=\{w\in L|\exists x\in G: |x|=2\cdot |w|\}$ is a context-free language? I think this could be a good exercise and the conditions are ...
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1answer
48 views

Grammar of words with exactly $k$ prefixes in another grammar

Given a context-free grammar $G$, how can one systematically construct a grammar $G_k$ such that $$ L(G_k) = \{w \in \Sigma^* : |\text{Pref}(w) \cap L(G)| = k\} $$ where $\text{Pref}(w)$ is the set ...
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1answer
58 views

Constructing PDA to accept language $\{a^ib^j \mid 0 \leq j \leq 2i\}$

How can I construct a PDA which accepts the language $\{a^ib^j \mid 0 \leq j \leq 2i\}$?
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1answer
42 views

Does left factoring CFG make it unambiguous?

I came across following problem: If the CFG is left factored then it must be Unambiguous and Not left Recursive. TRUE/FALSE? I have many thoughts about this. But I feel they are somewhat ...
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1answer
121 views

Who first introduced the pushdown automaton?

I'm interested in learning more about the history of automata theory and have tracked down many of the original papers on Turing machines, finite automata, and the like. However, I'm having trouble ...
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1answer
42 views

Constructing a pushdown automaton that accepts L*

Would appreciate if you could take a look at what I did and help me finish it. Given a pushdown automaton that accepts a language $L$ by final state, construct a pushdown automaton that accepts $L^*...
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1answer
31 views

Formal definition of an empty stack accepting PDA

PDA's are usually defined using the 7-tuple convention. $M=(Q, \Sigma, \Gamma, \delta, q_{0}, Z, F)$ F is the set of accepting states. I want to design a PDA accepting by empty stack, so using ...
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30 views

What is abstract machine for parallel multiple context free grammar (PMCFG)?

It is said, that PMCFG (Parallel multiple context free grammar) http://www.aclweb.org/anthology/P93-1018 is mildly context-sensitive grammar. My question is - what abstract machine can be used for ...
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1answer
42 views

Construct PDA for ${ \{0^m1^n0^{2n} | n>0\}}$

I have to construct PDA for ${ \{0^m1^n0^{2n} | n>0\}}$ So my idea is to (informally) not pushing anything into the stack while having 0s at first, then when automata start accepting 1s it should ...
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1answer
95 views

What is the set of languages accepted by empty stack pda?

I am having a confusion. Empty stack pda will always accept episilon. Therefore a language not accepting episilon will still be accept episilon, so how can we avoid this?
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1answer
45 views

Is the language $(a^n)^mb^n$ context free?

$(a^n)^mb^n$ for $m,n\ge 1$ This can be rewritten as $a^{nm}b^n $ i.e. number of $a$'s is a multiple of number of $b$'s, or for every m $a$'s there is one $b$. I thnk this language can be accepted ...
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1answer
38 views

Are there strings which get accepted only by PDA by empty stack and not by PDA by final state, and vice versa?

Can the same PDA accept both by final state and empty stack in the sense that there are some set of strings that are getting accepted by empty stack, while other set of string by final state and ...
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1answer
64 views

How to draw NPDA for words whose number of b's is strictly more than that of a's but strictly less than twice the amount

I know that CFG for $$ \{a^{m}b^{n}\mid m\leq n\leq 2m \}$$ is $$ S\rightarrow ab/abb/aSb/aSbb $$ but I am not able to tweak it in such a way that it is strictly in between m and 2m and not equal to ...
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3answers
217 views

why can not NPDA is equal to DPDA?

I have recently read that turing machine can be remodeled to perform as PDA now, i have a question that since DTM = NDTM ( non deterministic Turing machine) then every DTM can remodeled to be NDTM ...
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31 views

Building deterministic pushdown automaton for given grammar

I am trying to build a DPDA for the given grammar: $S \to aR$ $R \to bRT \ |\ \varepsilon$ $T \to cSR \ |\ \varepsilon$ I tried simplifying grammar first (removing null and unit productions, ...
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1answer
57 views

How prefix property of language affects the PDA

I know that every DPDA (deterministic PDA) is a PDA (more specifically, non-deterministic PDA). But I found it hard to understand, not that every DPDA is an NPDA, but some results that contradict this ...
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1answer
52 views

What changes need to be made to a Turing machine to make them equivalent to a PDA, a DFA?

I believe in order to make a Turing machine have the same power as a DFA (by power I mean all languages which a DFA can decided so can the Turing machine) we just don't allow any use of backtracking ...
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1answer
46 views

Context Free Grammer and PDA [duplicate]

So this a question from my book and I have to make CFG of this language but I am confused what does it mean when it says "L contains palindromes that don’t ever have the same character occur twice ...
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1answer
205 views

Context Free Grammer and PDA (Palindrome but without characters repeating in a row)

So this a question from my book and I have to make CFG of this language but I am confused what does it mean when it says "L contains palindromes that don’t ever have the same character occur twice ...
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1answer
44 views

Why is this pushdown automata for some palindromes right?

$B = \{w \in \{0,1\}^* | w^R = w, w \text{ length is odd} \}$ Solution: For example: $111$ should be accepted steps are $q_1 \to q_2$ stack: [$\$$] $q_2 \to q_2$ stack: $[\$, 1, 1]$ (using up $11$...
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1answer
277 views

PDA of the language where the number of a's are NOT equal to the number of b's

I have this NPDA for language L = {w: num_a(w) == num_b(w)} all loops in q1 ...
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What is the simplest automaton that can compute the sum of two integers of arbitrary length?

It should be obvious that a Turing machine is capable of computing the sum of two integers. However, what is the simplest automaton that can compute the sum of two integers of arbitrary length? I ...
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1answer
112 views

Construct a Deterministic Pushdown Automaton for unequal number of elements

Can anyone help me construct a deterministic PDA for the following language: $$L=\{w\in(a,b)^* \mid \#_a(w)\neq \#_b(w)\}$$ Or can anyone check if the following solution is correct?
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Why do pushdown automata use a stack?

I'm taking a computer theory class and my professor told us that a pushdown automaton cannot use data structures other than a stack (like a queue or multiple stacks). Why is that?
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1answer
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Convert grammar to Greibach form

The grammar is $S \rightarrow AA|a$$A \rightarrow SA|ab$The actual question is to find an NPDA accepting the language generated by this grammar but for that i firstly need to convert it into Greibach ...
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Which transducer models replacement in regex?

I am looking for the right transducer which allows to translate a sequence of literals into a sequence of same literals (or a subset of them) in arbitrary order. For example: ABC => CAB, which, with ...
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2answers
332 views

PDA to accept language with more a's than b's and c's

My question is similar to this one. I was wondering if a PDA exists, that accepts any words containing a's, b's and c's in a random order, where the total amount of a's is higher than the amount of ...
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1answer
142 views

Undecidable problem intersection of two DCFL languages is DCFL?

We have two deterministic pushdown automatas A and B, which languages are deterministic context-free. The problem is to decide if there exists a deterministic pushdown automata, which language is an ...
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1answer
127 views

Can PDA model Turing Complete objects if the objects' state are finite?

I am currently reading the extended Version of the Paper Online Detection of Effectively Callback Free Objects with Applications of Smart Contract. I am trying to understand the proofs of Chapter 6. ...
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Is there anything like equivalence classes in PDA (and more expressive ones, perhaps)?

The motivation for this question is the fact that partitioning DFA into equivalence classes is the mechanism that is used in model testing to generate test cases. However, obviously, DFA cannot ...
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1answer
45 views

$a_k$ is $\{L :\exists M$ a pushdown automaton with bounded stack of size $k$ which accept $L\}$ what is the set $\bigcup_1^\infty a_k$?

A related question: How to prove that a bounded pushdown automaton is regular? Well I proved that $a_k$ for each $k$ is the set of all the regular language. Thus $\bigcup_1 ^{\infty} a_k = \bigcup_1 ^...
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3answers
419 views

Are all finitely recursive context free languages parseable with a regexp?

Let's say I have a context free language. It can be recognised by a pushdown automaton. Chances are it can't be parsed with a regular expression, as regular expressions are not as powerful as pushdown ...
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1answer
104 views

How to convert a CFL to a deterministic PDA?

I am trying to complete this question. However, I am unsure of the steps necessary to complete the conversion from a CFL to a deterministic PDA. I know that $ww' | w \in \left \{ a,b \right \}^{*}, w'...
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1answer
107 views

Does a pushdown automata exists for the following language?

I have came across a question stating that language $L = a^n b^n c^{2n}$ is not a context free language and hence, no PDA can be constructed for it. But what I am wondering is that, if I add another ...
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1answer
27 views

Minimum number of letters

I have an assignment that I have to do and the question is Draw a DPDA that accepts the language L = {ba(bb)^(n+1)a^(n – 1) |n > 1}. Im not looking for the answer but rather some direction. I ...