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

learn more… | top users | synonyms

1
vote
1answer
64 views

If $L \cdot \{\epsilon, a, b\}$ is regular, is $L$?

Given that $L \cdot \{\epsilon, a, b\}$ is regular, is $L$ regular too? (Our alphabet is $\Sigma = \{a,b,c,d\}$ What I thought was yes, and here is why: If it is regular, then we know there ...
1
vote
1answer
219 views

Greibach normal form conversion

I'm trying to convert this into GNF: $S \rightarrow ASaa | bab$ $A \rightarrow Ba | bAB$ $B \rightarrow abba$ So I'm getting this, but I'm not sure understanding and applying correctly the concept ...
1
vote
1answer
359 views

Proving that $L= \{a^nb^n, n\ge 0\}$ is not a regular language.

The questions i'm 'stuck' on is: Let $\Sigma = \{0,1,2\}$ be the alphabet, and let $L$ be the collection of all the languages that contains only words that have even length. Prove that there are ...
1
vote
1answer
53 views

NFA from regular expression

I'm trying to make an NFA from the following regular expression. I'm not sure about the edges between nodes $q2$ and $q4$, maybe someone can point out where everything went wrong.
1
vote
1answer
27 views

Regular expression for a language

I made a regular expression to match this language but I'm not sure it's right. Perhaps someone can show me where it deviates. The language: $L = {a^{n} c b^{m} (cc)^{p} : n \geq 1, m \leq 1, p\geq ...
1
vote
2answers
164 views

interpreting language for finite state machine

Can someone explain to me what this means in clear english and maybe give me a hint for how to make a NDFSM (non-deterministic finite state machine) that accepts this language? I understand that the 3 ...
1
vote
2answers
98 views

The Relation of Cellular Automata to Languages

In Conway's Game of Life, would a cell be considered a deterministic finite automata? Is there a language for the automata, and would it be a regular language? In probabilistic cellular automata, are ...
1
vote
1answer
323 views

Best book for automata theory and compiler design?

I am currently pursuing my M.Tech in Digital Image Processing, I want to take admission in PhD program using subjects either Formal Language and Automata Theory or Compiler Design, Can anyone please ...
1
vote
1answer
942 views

Proof that equal-length-concatenation is a context-free language?

If A and B are languages, define A⋄B={xy | x ∈ A and y ∈ B and |x|=|y|}. For example, if A = {00, 101, 111} and B= {1, 11, 00110}, we would have A⋄B={0011}. Show that if A and B are regular, ...
1
vote
1answer
176 views

How to construct a context free grammar $G$ such that $L(G) = \{ a^i b^j c^k| j \gt i+k\} $?

How to construct a context free grammar $G$ such that $L(G) = \{ a^i b^j c^k| j \gt i+k\} $? I don't have much idea how to approach this one. Could some help me to understand how to approach these ...
1
vote
1answer
51 views

Can every regular language have a linear bounded automaton

As the question states: I am trying to understand automata. Can every regular language have a linear bounded automaton?
1
vote
1answer
767 views

Turing Machine Variation

Hi i'm trying to figure out this question: Give a formal definition of multihead-multitape Turing machine. Then show how such a machine can be simulated by a standard Turing machine Can someone ...
1
vote
1answer
209 views

How would I go about proving for this NFA?

I am struggling on this one question, where it is asking to define an XOR automata which is defined as an NFA and it is defined as the following: N accepts the string x if the number of distinct ...
1
vote
1answer
371 views

Finite state machine to report when the last 4 inputs were 1011

Suppose you want to construct an FSM containing one input and one output. Consider the example: The machine should assert the input (set to 1) when the last four bits taken in as input match the ...
1
vote
2answers
90 views

What are the states of this NFA?

I have to realize an NFA that recognizes the language of strings on the alphabet {a, b} ending with: bb, ba, baa. I thought that there must be the following states: $q_0$: the string ends with bb. ...
1
vote
1answer
476 views

Nondeterministic finite automaton proof

I am having a really hard time working the problem below out. I am not sure I am even on the right direction with this logic . Swapping the accept and reject states alone is not sufficient to accept ...
1
vote
1answer
79 views

Is this NFA correct for the language {w | w ends with an a and no a occurs between any occurrences of b}?

Language: {w | w ends with an a and no a occurs between any occurrences of b} The NFA must have exactly 3 states.
1
vote
1answer
1k views

Language that is recursively enumerable, but not recursive

I have a problem with this task: Show that this language is recursive enumerable, but not recursive: $L = \{ w \in \{0,1\}^* | M_w(x)\; \text{converges for some input}\; x \}$ (where $M$ is turing ...
1
vote
1answer
47 views

Show Two f.s.a. machines accept different input

I'm trying to solve it for two hours already. I know it somehow related to the pumping lemma Let $M_1 = \langle Q_1,S,f_1,s_1,F_1\rangle$ and $M_2 = \langle Q_2,S,f_2,s_2,F_2\rangle$ be two machines, ...
1
vote
1answer
1k views

Show two finite state machines are equivalent

Suppose $M_1 = \langle Q_1,S,R,f_1,g_1\rangle$ and $M_2 = \langle Q_2,S,R,f_2,g_2\rangle$ are two strongly connected machines. I need to show that $M_1 \equiv M_2$ iff there exist a state $p \in Q_1$ ...
1
vote
2answers
591 views

For the regular expression, (a* + b*) . (a.b)* , does the following automaton recognise the language it describes?

I constructed the automaton below using the assumption that the language described by the regular expression above only accepted the following strings: Empty, aabab, babab, aaaabab, bbbabab etc ...
1
vote
1answer
72 views

Proving $\{ll^{R}l|l\in\{a,b\}^{*}\}$ is not context free using the pumping lemma

How can I prove, using the pumping lemma for context free languages, that $\{ll^{R}l|l\in\{a,b\}^{*}\}$is not a context free language ? I tried to put $n$ as the pumping lemma constant and chose ...
1
vote
1answer
210 views

finite state machine is strongly connected

Let M be an n-state reduced strongly connected finite state machine. prove there exists an input string $w$, where $|w|\le n(n-1)/2$, s.t. M assumes each of its states at least once in response to ...
1
vote
1answer
259 views

Examples of epsilon transitions

I understand the meaning of epsilon transitions, but could someone give example where epsilon transition becomes handy?
1
vote
1answer
79 views

Regular expression arithmetics

What are the rules of regular expression arithmetics ? For example: Let $\Sigma=\{0,1\}$ $1. 1+01=(\epsilon+0)1$. $2. (\epsilon+00)^*=(00)^*$
1
vote
1answer
239 views

Random cellular automaton with three colors.

Does exist a Cellular Automata Rule that is RANDOM (like rule 30) and has 3 colors? I mean, as Wolfram says in his book, rule 30 shows a random behavior with some limits. But this happens using 2 ...
1
vote
1answer
121 views

What is this operation between sets {a, b}{c, d} do?

Not sure what this operation does, which is why i'm on here. It's not the cartesian product and no idea what it's called. I need to know to prove: For any language L, (Null set)L = L(null set) = ...
1
vote
1answer
1k views

Proving regular expressions to be equivalent

I'm trying to prove that two regular expressions are equivalent. I mean prove in the rigorous sense of the word (i.e. this is a legit proof). The process is to show that R1 is a subset of R2, and ...
1
vote
0answers
22 views

NFA that accepts binary strings starting with 1 and with at least 01, or at least 010, or both. [on hold]

Im not sure if I am understanding this question correctly. Its a problem without a solution in my text. Starting with 1, and at least 01 or at least 010 or both these substrings..... So a regular ...
1
vote
0answers
56 views

Does a mathematical construct exists which explains all theories?

If I am not wrong quantum mechanics is about measurements of different physical properties and probabilities of getting different outcomes. We have a mathematical construct to explain it, that is how ...
1
vote
1answer
21 views

is language accepted by finte state automaton

Hi I need to prove these languages are accepted or not by the following finite state automata. for 1 does this mean that we need an even number of a's or that a is literally 2,4,6,8....etc also ...
1
vote
0answers
34 views

Construct PDA that accepts the language $ L = \{ w \in \{ a,b,c\}^*; |w|_c=|w|_a + |w|_b \} $

Problem Construct PDA that accepts the language $ L = \{ w \in \{ a,b,c\}^*; |w|_c=|w|_a + |w|_b \} $ My first idea was this: There can be an "a","b" or a "c" at the beginning of a word Then we ...
1
vote
1answer
38 views

Construct a deterministic finite state automaton

Construct a deterministic finite-state automaton that recognizes the set of all bit strings that end with 10. This is what I drew. Not sure if its correct. State 2 is the final state. Am I missing ...
1
vote
1answer
32 views

Let $LOOP_{TM}$ be descriptor language of all touring machines that won't halt for any input. Show reduction of $HALT_{TM}$ to $LOOP_{TM}$

Question from Homework that I'm having difficult to answer on: Let $LOOP_{TM} = \{\langle M\rangle \mid \text{M is a TM that does not halt on any input w}\}$ Let $LOOP_{TM}$ be descriptor ...
1
vote
1answer
32 views

Is $L = \{0^{i}1^{i}0^{j}1^{i} | i, j > 0\}$ a context free language?

Is the following argument correct? $L = (A \circ B) \cap C$ where, $A = \{0^{i}1^{i}$ $|$ $i > 0\}$ $B = \{0^{j}1^{i}$ $|$ $i, j > 0\}$ $C = \{0^{i}1^{j}0^{k}1^{i}$ $|$ $i, j, k > 0\}$ We ...
1
vote
0answers
53 views

Where is my mistake in this DFA minimization?

I'm currently having trouble minimizing my DFA. I have the following graph: (ignore the numbers after ":") Using the table minimization method I reached: (x is distinguishable, O is ...
1
vote
0answers
62 views

Show that language $L'$ is regular given $L$ is regular

I show you some solution and I ask you for looking at it. $L'=\{y|\exists_{z,x} xyz\in L\wedge |x|=|y|=|z|\}$ Automaton for language $L$: $M=(Q,\Sigma, \delta, q_0, F)$ For language $L':$ $M'=(Q', ...
1
vote
1answer
36 views

Is the empty set/language contained in the following set

Assume I have the following set of languages: $$ \{L \subseteq \{0,1\}^* \mid \text{for all $w \in L$, $|w| \leqslant 3$}\} $$ I know it contains the language containing the empty word since the ...
1
vote
1answer
64 views

Prove that $\{ww^R\#ww^R\}$ is not context free

I need to prove that $L = \{ww^R\#ww^R \; | \; w \text{ is in } \{a,b\}^*\}$ is not context free. I have tried using the pumping lemma for this. For $w=a^pb^pb^pa^p\#a^pb^pb^pa^p$. I have two cases ...
1
vote
0answers
29 views

question about determinstic pushdown automata

i need to show that there is no DPDA accepts the language $L=\{a^n*b^n \mid n>0\}\cup\{a^n*b^{2n} \mid n>0\}.$ i used the prefix property but i'm stuck showing that if $w,w' \in L$, $w$ is ...
1
vote
1answer
160 views

Prove that $L=\{a^nb^nc^md^m \mid m,n >=0\}$ is context free language

I'm trying to write the grammar of this language, in order to prove that it is CFL but I'm stuck because m or n could be 0. The language is: $L=\{a^nb^nc^md^m \mid m,n >=0\}$ . If they were ...
1
vote
0answers
56 views

What is the highest state in the context of finite state automata?

I am doing an assignment for my Theory of Computation course. We are writing a function and I am having a hard time understanding what "highest" state means in the following context: ...
1
vote
0answers
149 views

Help with proving a language is regular (Sipser problem 1.49a)

I am working through Sipser's Introduction to the theory of computation on my own, so I don't have access to a teacher. Hopefully you can help me! Giving hints is highly appreciated. This question is ...
1
vote
0answers
64 views

Pumping Lemma for Context Free Languages: Is this language CFL?

I am learning for the first time the Pumping Lemma for CFL, and I thought I understood how it works until I came across this example: "Show that $L = \{a^m b^m c^n \mid m \leq n\}$ is not a CFL." My ...
1
vote
1answer
57 views

How to prove that a language `L` is not a regular language?

Given the following question: Prove that the following language is not a regular language: A language L in alphabet $\Sigma = \{a, b\}$ where every word ...
1
vote
0answers
30 views

how to create transition system/automata for modulo 4

I don't know how to think when to build a transition system/automata to calculate modulo 4 a of binary numbers. I know that the last two binary digits gives the rest but I need to go through hole ...
1
vote
0answers
48 views

Is this correct way to prove that { $uv$ $\mid$ $u$ and $v$ are strings over $(0,1)$ & $|u| = |v|$ } language is not regular?

I proved this using Pumping Lemma in the following way, Taking $p$ as pumping length then let us take a string $S$ where, $|u| = |v| = p$ Now according to pumping lemma $S$ can be split into three ...
1
vote
1answer
60 views

Constructing a NFA from a right linear grammar, is this correct?

Given the right linear grammar G S -> abA | bbB | a A -> bB | aA | b B -> baB | aaaA | [Epsilon/Terminates] Is the NFA in the image below the proper ...
1
vote
1answer
70 views

Difference between a*b and a*+b? Does the “+” denote Kleene plus or “or”?

Me and a friend are study for a quiz and are trying to determine the difference between the two NFA's produce by the regular exressions a*b and ...
1
vote
1answer
31 views

context free grammar that describes even numbers

I am learning about context-free grammars and as a toy example I wanted to design one that describes binary digits ending with 0. My attempt : S -> 1S | 0S | e0 - where e is the empty string. Is this ...