Questions tagged [pushdown-automata]
Questions about state machines with a single stack for memory. They characterize the class of context-free languages.
371
questions
0
votes
1answer
22 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 ...
41
votes
1answer
28k 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 ...
0
votes
0answers
50 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}^{...
-1
votes
1answer
65 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.
2
votes
1answer
124 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 ...
1
vote
1answer
65 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 ...
1
vote
1answer
417 views
Context free grammar for $bin(n)bin(n+1)^R$
It is pretty hard for me to understand, how binary representation of number may be context free. This language $L=\{bin(n)bin(n+1)^R : n \geq 0\}$ is context free.
Here, at 1.b, is a PDA which ...
0
votes
1answer
109 views
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-...
2
votes
2answers
698 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 ...
1
vote
1answer
43 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 ...
2
votes
0answers
803 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 ...
1
vote
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 ...
1
vote
1answer
152 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 $L$:
$\...
0
votes
1answer
499 views
Constructing a PDA with an unequal number of a/b
I'm looking at this pdf for problems: http://www.public.asu.edu/~ccolbou/src/355hw5solf10.pdf
I found question 3g to construct a pushdown automata for the following:
{$ {a^i b^j}$ | ${i \neq j}$}
...
1
vote
1answer
46 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 ...
0
votes
1answer
118 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
$\{a^ib^j \mid 0 \leq j \leq 2i\}$?
1
vote
1answer
226 views
CFG problem solved with PDA - looking for alternative solution
I'm trying to find CFG for the language $$L = \{ a^nb^mc^kd^l | n + k = m + l, (n,m,k,l) \in \mathbb{N} \}$$
and what I have done so far is to make PDA which simply does the following:
If on the ...
6
votes
1answer
259 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 ...
1
vote
1answer
49 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^*...
0
votes
0answers
35 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 ...
0
votes
1answer
84 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 ...
1
vote
1answer
60 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 ...
0
votes
1answer
202 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?
0
votes
1answer
47 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 ...
2
votes
1answer
102 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 ...
5
votes
3answers
9k views
Constructing a PDA for the language $\{a^m b^n : m < 2n < 3m \}$
I'm having a lot of trouble constructing a PDA for the language: \begin{equation*}
\{a^m b^n : m < 2n < 3m \}
\end{equation*}
I know if I push a symbol for each $a$ I see, then pop 2 symbols ...
-1
votes
3answers
1k 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 ...
1
vote
1answer
174 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 ...
0
votes
0answers
53 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, ...
1
vote
3answers
1k views
Push two symbols to stack at once in a push down automata
I am pretty new to PDAs and I was solving a problem which asked to design a PDA for the following: $a^n b^{2n}$.
The transitions on the PDAs I've encountered so far have pushed only one symbol onto ...
0
votes
1answer
104 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 ...
1
vote
2answers
648 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
vote
1answer
80 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 ...
1
vote
1answer
374 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 ...
1
vote
1answer
689 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
...
2
votes
0answers
90 views
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 ...
0
votes
1answer
225 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?
2
votes
2answers
162 views
Is the language with decreasing numbers of a, b and c context-free by pumping lemma?
So I've been given the following language on an assignment. It is the only question I have left of 10, and I've been racking my brains out trying to solve it for hours.
$$L=\{w:w\in(a+b+c)^*, n_a(...
-1
votes
1answer
178 views
Convert grammar to Greibach form
The grammar is $S \rightarrow AA|a$$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 ...
2
votes
0answers
84 views
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 ...
4
votes
1answer
313 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 ...
1
vote
0answers
12 views
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 ...
3
votes
1answer
68 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 ^...
2
votes
3answers
471 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 ...
1
vote
1answer
167 views
Nondeterministic PDA for the following language with Kleene star
I had a question regarding converting a language with the Kleene star production into a PDA. Here's the particular language I was looking at in my textbook:
$$L = (aaa^*bab)$$
My normal approach to ...
3
votes
3answers
10k views
Push down automata for $\{a^n b^n c^n | n \ge 0\}$
I am learning about context free languages.
I understand how $\{a^n b^n c^n | n \ge 0\}$ can be shown to be not context free using the pumping lemma for CFL's.
Intuitively however it seems that a ...
-1
votes
1answer
194 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'...
0
votes
1answer
137 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 ...
1
vote
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 ...
1
vote
1answer
189 views
Construct a pushdown automaton for $\{a^{2n}b^{3n}|n\ge0\}$
My idea is to (not formal) push an 'a' when we see an a, nondeterministically guess when n a's were seen from the input word, go to the next state. From there, when we see an a, push 2 'a's into the ...
