Questions tagged [finite-automata]

Questions about finite automata, an elementary automaton model with finite memory. It is equivalent to regular languages and the basis for many more complex models.

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Finding a finite automata that accepts a language that is the combination of two other languages with their own automata

I'm told that we have two DFA one A and one B both on alphabet $\sum$. I'm then told to define a DFA (5-tuple representation) with this condition {w | w = $a_i b_i$...$a_k b_k$ and all the $a \in A$ ...
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Proof for palindrome grammar by induction

I can't seem to find a solution Given is the following grammar for palindromes: $G_{pal}=\{\{a-z\},\{P\},P,R\}$ with $R:$ $P \to \epsilon \mid a \mid aPa$ for every a $\in \Sigma$ ...
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NFA that ends with 0 and doesn't have 11 after the first 0

So as the title says i m trying to find this NFA. So far i thought to make an NFA that "guesses" what comes after the first 0 and i got this: After some time trying to get rid of all the extra (7 !)...
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Why is this language a regular language?

Came across this in a book, and I'm wondering why the following language is regular? $$ L = \{a^nww^R: n \geqslant 0, w \in \{a,b\}^3\}$$ Is it correct to say that $$ \{a^n : n \geqslant 0\} $$ is a ...
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Regular expression for a palindrome of finite length?

I have a language $$ L = \{ww^R, w \in \{ab\}^5\}$$ I know this is a regular language because it is finite (since w can only be of length 5). I want to prove it's a regular language, so I'd create a ...
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1answer
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I'm asked to draw DFA for this {$\epsilon$, 0} however I do not understand what {$\epsilon$, 0} mean

I'm asked to draw a DFA of this {$\epsilon$, 0} but have no clue what it means. Can someone help me understand what the automata is supposed to do? I know that $\epsilon$ is the symbol for empty ...
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2answers
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can more than two arrows point towards the same state from other states in a DFA?

Is something like this possible: You have state A,B,C all pointing towards accepting state D. Is this allowed? Where online can I find a list of rules that define how an automata must be drawn or ...
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$\text{DSPACE}(O(1))=\text{REG}$ Proof?

I want to know why $\text{DSPACE}(O(1))=\text{REG}$, especially in the direction of why all languages in $\text{DSPACE}(O(1))$ can be recognized by a finite automaton. I've thought for some time and ...
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Converting CFG to GNF problem

I have a big problem with converting GNF example. This is my CFG $ S \to AS\mid BS\mid \lambda\\ A \to aC\mid BCA\mid c\\ B \to AB\mid b\mid \lambda\\ C \to S\mid d $ I simplified the CFG by ...
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1answer
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State complexity of converting epsilon-NFAs to NFAs without epsilon transitions

I am well-aware of the result showing that one can convert an epsilon-NFA (that is, an NFA with epsilon transitions) $A$ to an NFA without epsilon transitions $A'$, where $L(A) = L(A')$. Is there a ...
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Automata that respect the condition {w|w contains at least two 0s and at most one 1}

we have the alphabet {0,1}. {w|w contains at least two 0s and at most one 1} It tried this: (However I'm not sure if it's correct. If it's incorrect why?)
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I'm trying to understand DFAs is my DFA correct in this question if not why?

I have the following alphat {0,1}. I'm told to draw a DFA which fulfills the following: {w|w starts with 1 and ends in 0} This is the DFA I came up with.
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How to create a regular expression for this language?

I have a language: $$ \{a^jb^k \mid j \neq k \text{ and } j \equiv k \pmod 3 \}$$ I want to prove that this language is regular. My first thought was to create a regular expression that accounts for ...
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Are DPDAs accepting on final state equivalent to DPDAs accepting on empty stack equivalent? [duplicate]

Say I have a string x that is accepted by some DPDA P that accepts empty stack. Intuitively it's seems impossible for P to accept any string x.y for any y != epsilon. The below DPDA accepts on final ...
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Chomsky hierarchy for finite state transducers

In this question in the first answer someone mentions a "special transduction hierarchy". I cannot find anywhere anything about it. Could someone point me to resources on this topic?
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Turning a regular expression into a DFA

i'm studying for an exam i'll have soon and i don't understand how to draw a DFA for a regular expression, i asked my professor by mail but he doesn't asnwer... In the courses available on my college'...
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Minimization of automata with dead state

I am supposed to minimize the following DFA automa, which contains dead state: But after the minimization of the automata, it stayed the same. Is it correct?
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Two-way finite automaton: How does the automaton remember the state

I have been going through a theory of Two-way finite automatons and I did not understand the given example when there were a DFA A = (Q, Σ, δ, q1, F). the 2-DFA B = (Q ∪ Q| ∪ Q|| ∪ {q0, qN, qF}, Σ ∪ {#...
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Turing Machine state going to itself

Hey guys in a turing machine can a state go to itself by reading a letter. For example, q2 reading a 'c' to go to itself. Is that possible? Or does it need to read a tape alphabet, such as $ to ...
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1answer
47 views

Conversion of nfa with self-loop to one without self-loop

For every nondeterministic finite state automata that has self-loop(s), there exists an equivalent nfa that does not have any self-loop. How can we prove this statement in a general basis without the ...
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How to generate a DFA that recognizes a non-regular Grammar

How would you convert the following grammar to a DFA that recognizes its language? \begin{align} &G = (\{S,A,B\},\{0,1\}, S, P)\\ &P\colon &&S\rightarrow A1B\\ &&&A \...
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Multiple paths for a accepting string in NFA?

If a string(w) is accepted by an NFA, then corresponding to w, can there be multiple paths each starting from the start state and ending at an accepting state?
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Automaton-based model checking on finite traces

I want to check whether a formula in finite LTL is valid on a finite, linear trace. For infite traces I would create a Kripke structure of the trace and a Büchi automaton for the negated formula, ...
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1answer
22 views

Construct regular expression that contains the substring

I need to write a regular expression for the following set of strings on Σ = {a, b, c} in which the number of b’s is even, and contains abcba as a substring. So far, the even number of b's can be ...
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If T is a Turing Machine, what are the languages Accept(T), Reject(T) and Loop(T)?

I have the following Turing machine: I am asked what are the langauges accept(T), reject(T) and loop(T). This seems to me a trivial question as from the looks of it, accept(T) is the language of all ...
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Construct a DFA with reduced states equivalent to 10 + (0 + 11)0*1

I have found this question in a book. I could convert it into its equivalent DFA. But the problem is with the "reduced state" part. I think the answer given in the book is wrong. What would be the DFA ...
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2answers
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convert RE to NFA

The Regular Expression i am having trouble with is the following a(b|bcc*)*c. My main concern is what do i do with the c*? I can lay the rest of the diagram correctly (i think) but that part is ...
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Minimisatiom using Myhill-Nerode Theorem

I have recently studied the Myhill–Nerode theorem and while applying it to minimize these FSMs, I encountered a problem. Is it always the case that the final states should be grouped together because ...
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Constrained (linear) NFA-epsilon to DFA conversion

Goal: convert NFA -> DFA Overall goal: see if the intersection of 2 of these NFAs is empty. This will be done by converting to DFAs then DFA intersection. input NFA: multigraph between states (each ...
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1answer
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Path NFA-eplison to DFA conversion

Does a path (as in path graph or linear graph) NFA-epsilon have a simpler or more efficient algorithm other than the subset construction to convert to a DFA? The only simplifications I have come up ...
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2answers
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Proving non-regular language using the pumping lemma

I would like to verify that the following language is not regular. I know that if the pumping lemma is not valid then the language is not regular. (but its not enough to prove that the language is in ...
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If L is regular language then each equivalence class is also regular?

L is a regular language. Let's say that E is one of L's equivalence classes - is it true/false that E is also regular? The equivalence relation is, from Wikipedia: "Given a language L, and a pair of ...
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1answer
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FA for |w| divisible by 3 or number of zeros divisible by 2

Working on a question were I should construct a deterministic finite automaton for the language $L=\{w\in \{0,1\}^* \mid |w| \mod 2 =0 \lor |w|_0 \mod 3 =0 \}$ The DFA for the two sublanguages is ...
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What strings does this language accept/reject?

F = {ww | w ∈ {0,1}^*} Which strings are accepted and why? 0011 1010 1111
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Over the alphabet {a,b,c,d}, how would i construct a NFA that only accepts strings that end with a letter that is already part of the string?

I've been trying to create a NFA that accepts strings that end with a letter that exists in the string. For example abcdb, cbdd, acac etc. while strings like abc aacd etc are not accepted since the ...
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1answer
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Languages such that DFA requires $\Omega(c^k)$ states but NFA needs only $O(k)$ states?

Given an alphabet $\Sigma$, let $c=|\Sigma|$. Can a set of languages $\{L_k\}$ be created, such that any DFA for $L_k$ has $\Omega(c^k)$ states and a NFA for $L_k$ exists with $O(k)$ states? I'm ...
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Convertion from NFA to DFA

I have converted nfa to dfa. But when I checked with some examples, it looks like it is wrong. ...
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1answer
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Prove that a language is decidable

I need some help to prove that the language is decidable. $K$ = {$N$ : $N$ is a DFA (Sigma = {a, b, c}) and $L$($N$) contains at least one word in which there is no a}. It tried to make an algorithm ...
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Clarifying Practicality and Usage of a DFA's Accepted Language

I was reading up on DFA's and their accepted languages when I stumbled across this: Let a DFA $M$ accept the language $L⊆Σ^∗$, DFA $M'$ accepts $P(L)=$ {$w∈Σ^∗|wy∈L$ for some $y∈Σ^∗$}. Since any $wy$...
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Prove if {a^i b^j | i ≤ j} is a regular language or not [duplicate]

How can i prove if this language is regular or not? (i think is non regular)
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Why does a DFA have multiple final states?

I am taking a course on programming language design and we got to the DFA part. It is known to be formally defined by a 5-tupple but they did not make it very clear to us why a DFA can have multiple ...
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3answers
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An approach to determine whether language is regular or not?

I have the following problem. I need to determine whether this language is regular or not: $L:= \{ w \in \Sigma^*: \forall \alpha ∈ \Sigma, |w|_\alpha \text{ is even or divisible by 3}\}$ $|w|_\...
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Is this a valid DFA for (a|b)*abb?

I'm trying to come up with an alternate DFA for accepting (a|b)*abb than the one present in the dragon book. Here's the one I tried: It seems valid to me but I'm ...
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How to prove this language is context free?

There's lots of ways to prove a language is not context free. Going through some exercises, I'm stuck at a question that asks me to prove that a language is indeed context free. $L = \{a^{(n+1)} b^{(...
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can a DFA with only final states be minimized?

I need to construct a DFA for a certain language with as little states as possible. so far my "best" solution contains 15 states. however, people claim it is doable in 7 states only. I tried for ...
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2answers
50 views

Usual distances on DFAs (Deterministic Finite Automata)?

I've been searching in the literature for examples of distances defined on the set of the DFAs (or on the set of minimal DFAs) that are defined on a given alphabet sigma. Since the languages they ...
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Prove that regular languages are closed under Kleene star [duplicate]

Given $L$ is a regular language, how can I prove that $L^*$ is a regular language too? I've constructed an NFA which contains a new initial state that has an $\epsilon$-transition to the original ...
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1answer
34 views

Minimizing DFA built on set of words

A set of English words is given. Is there linear or sublinear algorithm to build minimal DFA for the given dictionary? I tried different approaches, and they all were concerned with building Trie and ...
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How to write regular expression [duplicate]

The set of all strings over {0,1} such that every block of 4 consecutive symbol contain at least two 0's Can you guys tell me what is the correct answer for this ?
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McNaughton-Yamada Algotihm (1960) Regular Expression to DFA without passing through NFA

I have a homework problem here. It asks me to use the McNaughton-Yamada algorithm to first convert a regular expression to a DFA, and then minimize this using a partition argument. I can do the latter....

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