Automata Theory, including abstract machines, grammars, parsing, grammatical inference, transducers, and finite-state techniques

learn more… | top users | synonyms

0
votes
1answer
35 views

How can a DFA corresponding to an NFA have a transition that the original NFA does not?

First sorry for the poor pictures, but I think they are ok enough to get the point across. I would like to see the steps involved to convert this NFA to a DFA using the method explained in this ...
0
votes
0answers
133 views

DFA for language accepting odd number of a's and each a followed by at least 3 b's

I am creating a DFA for a language (over alphabets {a,b}) that accepts all strings containing "odd number of a's and each a followed by at least 3 b's" . This is what I've gotten so far with q4 as the ...
0
votes
0answers
38 views

Number of states of a finite automaton recognizing all words beginning with some fixed string $x$

For a string $x \in \{a,b\}^\ast$ with $|x| = n$, how many states are required for an FA accepting the language of all strings in $\{a,b\}$ that begin with $x$? For each of these states, describe the ...
0
votes
1answer
40 views

Pushdown Automata and Challenge in Grammar

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$\epsilon$ ...
0
votes
0answers
44 views

Every DPDA has an equivalent DPDA that always reads the entire input string

I am trying to understand the proof from Michael Sipser's Introduction to the Theory of Computation, page 132. I don't understand why if $q \in F′$ then $\delta(q,a,\$)$ is set to ...
0
votes
1answer
46 views

A CFG Grammar for One Language

Suppose : $w_1,w_2 \in \{a,b\}^∗$ and $ L=\{w_1w_2 \mid w_1,w_2 \in \{a,b\}^* \land n_a(w_1)=n_b(w_2)\}$ $n_a$ is number of $a$'s and $n_b$ is number of $b$'s. This is a Entrance Exam question. I ...
0
votes
0answers
38 views

Language of Specific Grammar

I ran into this exercise in Sipser's Note on Computation Theory. Consider the following grammar $G$: $$\begin{align} S &\to aSD \;|\; bB \\ D &\to dS \;|\; a \\ B &\to bB \;|\; ...
0
votes
1answer
25 views

Algorithm that takes input desc. of two PDAs and outputs intersection of langs. recognized by two PDAs

Does there exist an algorithm which takes as input the descriptions of two pushdown automata, $P1$ and $P2$, and prints the description of another pushdown automaton which recognizes the intersection ...
0
votes
1answer
21 views

Deciding TM which fails to halt whenever the length of its input string is a prime number

I have the following Statement: "A TM called $A$ which fails to halt (i.e runs forever) whenever the length of its input string is a prime number, and eventually halts for all other input strings" ...
0
votes
0answers
29 views

Design an finite automata for 010 and 01? [duplicate]

I have tried below question for designing automata but didn't success . ...
0
votes
0answers
15 views

What are the classes in A.N. Maslov hierarchy of indexed languages corresponding to Chomsky Hierachy?

As we know,that classes in A.N. Maslov hierarchy of indexed languages of level 2 is in sensitive languages of Chomsky hierarchy. What are the classes in A.N. Maslov hierarchy of indexed languages ...
0
votes
0answers
27 views

Do automatons and formal grammars belong to formal systems

A formal system consists of a formal language, a formal grammar that generates the language, a set of axioms, and a set of inference rules. Are automatons also formal systems? Is an automaton ...
0
votes
0answers
149 views

How to check whether a language is regular or not?

Say I have a given expression like $L_1\{a^n\mid n\ge0\}$ $L_2\{b^n\mid n\ge 0\}$ Then what is the procedure of checking weather L1.L2 is regular or not?
0
votes
1answer
32 views

How does the push-down automaton have to look like?

Could you give me a hint how to find a push-down automaton for the language: $$L=\{ a^n b^{2n} | n \in \mathbb{N}\}$$ How does the push-down automaton have to look like?
0
votes
0answers
16 views

Struggling to prove Markov chain property / State machine property - I can see what I need to do just can't write it

First notation, I have created the shorthand: $$P_x(A)=\mathbb{P}(A|X_0=x)$$ just to save time. I wish to prove "Lemma 1.3" which states the following: If $0<\alpha\le P_x(T_y\le k) \forall x\in ...
0
votes
2answers
40 views

minimal DFA with four states

I want to minimal this DFA: But i don't know what to do. Anyone can help me? Thanks
0
votes
1answer
51 views

What did the proof by diagonalization actually disprove?

http://www.cse.ohio-state.edu/~gurari/theory-bk/theory-bk-fourse5.html I sort of understand the proof, but is it showing that some language are undecidable? If so, what language exactly? Because each ...
0
votes
0answers
45 views

CFG Convertion to GNF

I have a very simple CFG that I am trying to convert into GNF. The CFG is: S -> aSbS S -> epsilon I looked at the CFG and I think I can just do the ...
0
votes
1answer
63 views

Backus-Naur Form with automata

Parsers & compilers usually utilize deterministic finite automata to parse input. It's very easy to implement a generic DFA tool, that simulates any DFA table for example to validate input. ...
0
votes
1answer
69 views

turing machine accept and reject state

I am pretty new to Turing Machines and I am trying to understand the basic things first...so my question is , would this machine accept all words ending in 'a' ? if ...
0
votes
0answers
55 views

how do I make this post machine accept aab or baa?

so far I made it accept, a, aaa,bab but now I want strings aab or baa. How would I do this ? this is what I have so far... edit: @Hagen von Eitzen here is the example of Post Machine that a lot of ...
0
votes
0answers
52 views

Is the language $L = \{0^m1^n: m \neq n \}$ not context free?

I have been trying to prove that this is not a context free language using the pumping lemma for CFLs. I have tried for hours but am not able to prove it. Is it a context free language or not? How to ...
0
votes
2answers
40 views

DFA Construction with three strings in language

Draw DFA that recognizes the following language, with the alphabet {0, 1} {0011, 11, 0101} I'm having a lot of trouble with this, because I know DFA have to have a determined path from each state ...
0
votes
2answers
62 views

Pushdown Automata

I having trouble constructing NPDAs for these two languages: $L_1 = \{a^nb^m \mid 2n \le m \le 3n\}$ $L_2 = \{a^nb^mc^k \mid n = m \: or \: m \ne k\}$ Would these be the proper states for the first ...
0
votes
0answers
32 views

Context-free languages

Is the following language context-free? $\{ w \in \{a,b,c\}^* : (\#_a(w) - \#_b(w)) \cdot \#_c(w) = \#_b(w)$ and all c's are encountered before any a$\}$. $\#_a(w)$ = amount of a's in w Thanks in ...
0
votes
1answer
21 views

Eliminating Unit Productions

Eliminate all unit-productions from the grammar: $S \rightarrow abA\:|\:A\:|\:B$ $A \rightarrow B\:|\:ba\:|\:aBA$ $B \rightarrow A\:|\:aa\:|\:aA$ An article I was reading said that a unit ...
0
votes
1answer
22 views

Are these two languages equivalent?

$L = \{w \in \{a,b\}^{*}$ such that $w = R(w)\}$ R(w) = the reverse of w $L = \{u \in \{a,b\}^{*}\}$ If not can you draw a pda or define a grammar for each? I don't see how they could have ...
0
votes
0answers
80 views

how to convert Finite Automata into Push Down Automata

I am trying to convert Finite Automata into Push Down Automata and I am not sure if I am doing this right. There are not many good tutorials on this topic that I can find, but this is what I have. I ...
0
votes
0answers
54 views

Cartesian product of a DFA and PDA

I am just wondering how to do it. I am not quite sure if this is the right way. 1) Write down all the combination of states. 2) Take into consideration the "input" side of the DFA and write the ...
0
votes
0answers
24 views

Designing a pushdown automata

I think I realized something, but I am not sure. So what I think I've realized is that if you have to design a L such that it accepts any string with the same amount of 1 and 0. You need 2 states: ...
0
votes
1answer
41 views

Prove L is not a regular language (A Finite State Automaton cannot accept it)

$$\mathscr L = \{x \in \{0,1\}^* \mid \text{there is a } y \in \{0,1\}^* \text{ such that } x = yy\}$$ How can I prove that this is not a Regular language? I tried using proof by contradiction but ...
0
votes
0answers
38 views

Is this grammar ambiguous?

$S > SS|10|0$ $S > SS > SSS > 0SS > 00S > 000$ $S > SS > 0S > 0SS > 00S > 000$ $2$ leftmost derivations
0
votes
0answers
37 views

Relationship between pushdown automata and CFG

I thought that pushdown automata and CFG were separate things in that one was the graphical expression of the other, but I saw a pushdown automata that uses CFG terms such as epsilon, S, S->1S0, or ...
0
votes
1answer
43 views

Proving that a language having a particular CFG grammar is equivalent to a particular L

I think we need to prove that L(G) is a subset of L and then we need to prove that L is a subset of L(G). For the first part, I think we need to say for any w in L(G) we have an even number of as ...
0
votes
1answer
22 views

Pumping lemma clarifications

http://www.cs.oberlin.edu/~asharp/cs383/handouts/pumping.pdf I came across this and realized that what some people told me was completely wrong. We get to choose xyz, but the demon choose uvw and uvw ...
0
votes
1answer
74 views

How do we choose a good string for the pumping lemma?

we have a Language $$\mathscr L: \{a^mb^n: m \ne n\}$$ we need to choose a good string $w$. apparently $w = a^{n+1}m^{n}$ is not a good string. can someone explain why? I also found this and I ...
0
votes
1answer
48 views

Struggling with Proof Writing. Simple question for demostration.

I am practicing writing proofs over regular expressions. Here is the question: Show that $(r\cup \varepsilon)^*= r^*$, where $r$ is a string. Intuitively, the left hand side is the concatenation of ...
0
votes
1answer
260 views

Context free grammar to pushdown automata…

<expr> −→ <term> | <expr> + <term> <term> −→ <factor> | <term> × <factor> <factor> −→ (<expr>) | b ...
0
votes
1answer
27 views

If the language is context free?

i believe intuitively the following language is CF. But there is a book (without more description) that states the language is not CF. If I'm in a wrong way? $L=\{W_1cW_2 | W_1,W_2 \in (a+b)^* W_1 ...
0
votes
1answer
41 views

Regular language restricted to smaller alphabet is regular

Let $L$ be a regular language on some alphabet $\Sigma$, and let $\Sigma_1 \subset \Sigma$ be a smaller alphabet. Consider $L_1$ the subset of $L$ whose elements are made up only of symbols from ...
0
votes
2answers
41 views

What method should you follow to show what a DFA does?

I'm specifically looking for help analyzing the following DFA. What steps would one follow to show what language this particular DFA accepts? To me it seems quite random, and I can't figure out a ...
0
votes
0answers
59 views

Is the PDA I drew correct?

Could you tell me if the language $L=\{a^{m}b^{n}:m \neq n,m>0,n>0 \} $ is accepted by the following pushdown automaton, where the alphabet of the stack is $\{a,z\}$ and $z$ is the initial ...
0
votes
2answers
61 views

Determining whether a language belongs to R or RE (Turing Machines)

Does the language L belong to R, RE or neither? In each case, why? Thanks a lot!
0
votes
1answer
51 views

build finite automaton for language minimize states

I want to build a finite automaton that accepts $a^nb^n, n \gt 0, m \ge 0$. I can't do it unless the FA has two final states, i.e.: $delta(q0, a) = q1 delta(q1, a) = q1 delta(q1, b) = q2 delta(q2, ...
0
votes
0answers
42 views

Context-sensitive grammar for this language

In order to write a context-sensitive grammar for: $L = \{ a^{n} b^{n} c^{n} d^{n} : n \ge 1 \}$ One possible set of productions is: $S \rightarrow aBCd | abcd $ $aB \rightarrow aaBb | ab | ...
0
votes
1answer
48 views

Assign Integer to Each Turing Machine

I have the following problem: suppose that we have an infinite set of symbols, $A = \{a_1, a_2, ...\}$ from which all Turing Machine input alphabets are chosen. Show how we could assign an integer to ...
0
votes
2answers
36 views

Turing decidable/undecidable

let $X = \{\langle M \rangle\ |\ M\text{ is a finite state machine and }L(M) = \emptyset\}$ where $\langle M \rangle$ is an encoding of the machine $M$. can you prove whether $X$ is Turing ...
0
votes
0answers
31 views

Is this a context-free language?

Let $L = L_1^* \circ L_2^*$ where $L_1 = \{1^n 0^m 1^n : n,m \in \Bbb N\}$ and $L_2 = \{0^m 1^{2m} : m \in N\}$. Is the language $L$ a context free language? I think I can write automata for $L_1$ ...
0
votes
0answers
36 views

How to write a Regular Expression

I have seen that the regular expression for the set of strings beginning with a and ending with b is written as a(a+b)*b Can some one tell me how to write this
0
votes
1answer
214 views

Grammar Construction from Given Language!

Just a fast question! I have this language L(G) = { z^n * x^2n with n>=1 } What is the grammar ? I think it should rather be: ...