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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How specifically do I need to describe (in words) the language of a regular expression?

For the regular expression $(a*ba*b)*a*$, I want to learn how to describe it in words. I know there are an even number of $b$s but how much do I need to explain it? Do I need to explain it enough that ...
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How many different languages over the unary alphabet {a} are recognized by 2-state DFAs?

I am struggling to answer the following question: How many different languages over the unary alphabet {a} are recognized by 2-state DFAs? According to the textbook, the hint was to first ...
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Is this language over 0s and 1s regular?

The language L = {xyx, where x,y are arbitrary strings over {0,1}}. Is this a regular language? How can this be shown?
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Can a DFA have an unreachable state?

I am trying to prove or disprove the following statement: If $A = (\Sigma, Q, \delta, q_0, F)$ is a complete DFA where $F \neq \emptyset$ then $L(A) \neq \emptyset$ So my initial thinking is to ...
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Which of these languages is regular? The Pumping Lemma seems to show none are

I've been reviewing past paper questions for an automaton course, and came across a question which effectively asks, which of these languages is regular? $$ \{\ 0^m1^{(m \times n)}0^n\ \colon\ m,n\ge ...
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1answer
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NFA equality for automata with partial transition functions and all states accepting

Given two nondeterministic finite state automata with partial transition functions, such that all states are accepting, except for the implicit failure sink state, is it possible to decide in ...
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1answer
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How to construct a DFA which accepts all the strings endig with aa and no two consecutive b (bb)

I have to construct a DFA which ends with aa and does not contain any pair of b-s. A = {a,b}, {aa,baa,aaa,abaa,babaa,...}. I know how to construct them as separate DFAs but not together merged.
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Deterministic Finite Automaton

design a DFA accepting the set of strings over the alphabet {0, 1} that when interpreted in reverse as a binary integer, are divisible by 3
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1answer
45 views

Kleene star operations

Let $𝚺$ be any alphabet and let $𝑳_𝟏 \subseteq 𝚺^{∗}$ and $𝑳_2 \subseteq 𝚺^{∗}$ be two non-empty languages. a. If $𝑳_𝟏 𝚺^{∗} \neq 𝚺^{∗}$ than what can we say about $L_1$. b.Let $\Lambda \...
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1answer
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Need help with previous “Automata / Theory Of Computation” exam question

I passed by this question in a previous exam while studying for the "Automata / Theory Of Computation" and I am struggling to find answer. I would appreciate it if someone can help me with it: This ...
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1answer
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Finding the union, subtraction, and intersection of two DFAs

I recently solved problem of finding union of two DFAs and came up with some observations. I need confirmation about them along with some other facts: I can prepare the union, subtraction and ...
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PSPACE-completeness of DFA intersection problem

Let some deterministic finite automata be given. There is a problem of determining whether the intersection of these DFA is empty, and I want to show its PSPACE-completeness. It seems to me that I ...
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When Turing Machine behaves like Finite state automaton

I read following: Turing Machine with finite (fixed sized) tape is essentially Finite state automaton. Is this fact correct? My doubt is Turing Machine can go infinite loop even on finite tape if ...
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1answer
92 views

Prove/disprove: If $𝐿_1$ is a finite language but not empty and $𝐿_2$ is NOT regular then $𝐿_1 \circ 𝐿_2$ is NOT regular

That what I have so far, but I am not sure at all. Assume toward contradiction that $𝐿_1 \circ 𝐿_2$ is regular. Define $\Sigma' = \{\sigma'|\sigma\in\Sigma\} $. Define a regular substitution $\...
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Are every 2 DFAs with $n$ states for a language $L$ isomorphic to each other?

Consider 2 DFAs both determining a language $L$. Both DFAs have the same number of states $n$. Can I then conclude that these two DFAs are isomorphic? I think the answer is yes, because if I'd make ...
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DFA that accepts all the strings that either begin or end (or both) with 01

I came across following problem: Minimum number of states in DFA that accepts all the strings that either begin or end (or both) with 01 over the alphabet {0,1} = ? I first tried to prepare two ...
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Are DFAs with a unary alphabet strictly less powerful than DFAs with a binary alphabet?

Are DFAs with a unary alphabet strictly less powerful than DFAs with a binary alphabet? Is this even a meaningful question? For example, if $\Sigma = \{\texttt{0}, \texttt{1}\}$, we can encode any ...
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DFA question regarding memory and states

I have to program a DFA which has to do the following for an input of binary 5 my task told me to use a finite memory 0 0 1 1 2 3 2 4 0 3 1 2 4 3 4 qi−1 δ(qi−1,0)...
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1answer
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Copy operation in under 9 states?

There is a long row of cells. Each cell contains 0 or 1. A machine is positioned immediately to the right of a series of uninterrupted 1’s followed by an uninterrupted series of 0’s. In the following ...
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Length of strings accepted by DFA

Problem: Given a DFA $D$, find all possible lengths of strings accepted by the $D$. It makes sense that these lengths can be represented as $a_i+kb_i$. What might be the algorithm to find all such ...
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1answer
43 views

How create DFA with multiple finished states for lexers?

Is possible to create DFA directly from regular expression. But for lexical analyse is needed "joined" DFA with many finish states, for example one state for string, one for integers, one for floats ...
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NDFA has maximum states as 2^n the same for qubits in quantum computation.How they can be distinguished in means of computation? [duplicate]

I am a Computer Engineer. I studied basics of Quantum Computation. In dealing with multiple states, I feel NDFA does similar to Quantum Computation but we preferred to convert NDFA to DFA and solved ...
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Regularity of language of words of prime length [duplicate]

Is the following language regular? $$ L_{\mathit{prime}} = \{ w \in \{0,1\}^* : |w| \text{ is prime} \}. $$ I have to either provide a DFA (if the language is regular), or prove that it is not ...
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1answer
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Language to regex

Let A={a,b}. So the question is to write regular expression such that L(r) which consists of all words. My answer is this: L(r)= (a+b)* a* b* (a+b)* Is this ...
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Deterministic pushdown automaton for a given language

I am trying to make a deterministic pushdown automaton from this language but without success. Here is the language definition: $\ L=\{0^n 1^m a^i b^j \ /\ m,n,i,j > 0 \ and \ m+n=i+j \} $ ...
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1answer
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Why does $L = \{ 0^n 1^n \space | \space n \in \mathbb{N} \}$ belong to $\mathrm{P}$?

My professor said that the non-regular language $L_{1} = \{ 0^n 1^n \space | \space n \in \mathbb{N} \}$ belongs to $\mathrm{P}$. I do understand that all regular languages belong to $\mathrm{P}$ as ...
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2answers
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Does any algorithm loops at some point?

Given that any implementable algorithm has a finite number of internal states, and given that any state is determined by the previous one, does that implies that any algorithm loops at some point? If ...
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1answer
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Converting DFA to RE with Arden's Rule

So I've searched around and found the algorithm to do so: How to convert finite automata to regular expressions? and I decided to test out the second-level response, Raphaels, and while I was getting ...
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1answer
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Can nfa consume more than one letter at a time

If I have a NFA/DFA and I expect inputs of 00, 01, 10, 11 can I read input in groups of 2 binary digits at a time. like the example shown
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NFA/DFA for $ L= \{a^n b^n a | n\ge0\}$

I have made two DFA’s for $ L= \{a^n b^n a | n\ge0\}$. First one has several states. The second one is accepting an empty string also. Somebody please guide me the correct one. Zulfi.
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Regular expression containing lambda

What is the meaning of lambda here: $$(b+c)^*(a+\lambda)(b+c)^*(a+\lambda)(b+c)^*(a+\lambda)(b+c)^*$$. I know that lambda is used in the context of NFA? Let's suppose we break down the expression ...
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Intersection of two DFA's

I am trying to understand the intersection of 2 DFA's. I got the following link: Intersection of 2 DFAs I can't understand why they have not used the symbol 'b'. In the DFA's they have symbol 'b' also ...
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What exactly is “pattern matching”?

I know some examples of "pattern matching". E.g. in the context of functional programming, and regular expressions. But is there a precise definition? In particular, it seems that it has to do with ...
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Meaning of $a\lor b \to b' \lor c'$

So I have done part a) but I have no clue what I am supposed to do for part b), I have been trying for days to wrap my head around and even asked my fellow course mates, none of which seem to know ...
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Use ML to create a graph

I'm currently looking for literature/papers on machine learning techniques to create structures. In detail, I want to generate finite automata (NFA, DFA), which are useful for student-exercises. So I ...
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1answer
84 views

Determine if an NFA accepts infinite language in polynomial time

Question Statement: Given a NFA $N$, design an algorithm that runs in polynomial time such that it determines if $L(N)$ is infinite. (Note that converting NFA to DFA is exponential time). For any DFA,...
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Why does this finite state machine state transition diagram solution has more states than my solution?

I can't figure out what is wrong with my solution and why does it differ from book's solution. I think the only thing that matters is the previous state of A so that there should be two states, one ...
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Possible number of DFAs, NFAs, DPDAs, NPDAs, NDTMs and DTMs for various input parameters

I came across problem asking for possilble number of DFAs for a given number of states and alphabet. I started guessing if we can find possible number different automatas for given number of states, ...
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1answer
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No nonfinal states in NFA

I know that if there are no non-final states in DFA then the language accepted is $\Sigma^*$. What will happen if there are no non-final states in an NFA? Can we say it also accepts $\Sigma^*$? Can ...
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Pumping Lemma with Prime Number [closed]

$\text {Could someone please help me with this proof: }$ $L:=\left\{a^{n} d^{m} b^{k} | n, m, k \in \mathbb{N} \wedge m \text { is a prime number}\right\}$ $\text {Maybe we can say, that } w=a^{n}d^{...
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1answer
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Closure of regular languages under “inverse second half”

Theorem. Show that if $L$ is regular, then so is $$ \varphi(L)=\left\{w \in \Sigma^{*} \mid \text {there exists an } \alpha \in \Sigma^{*} \text { with }|\alpha|=|w| \text { and } \alpha w \in L\...
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Minimal DFA for “$n$th character from the right is $a$” [duplicate]

I am given the following regular expression, which accepts all strings over $\{a,b,c\}$ whose $n$th character from the right is $a$: $$ (a|b|c)^*a(a|b|c)^{n-1}. $$ The exercise asks for the number ...
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1answer
50 views

Regular expression for language that does not accept x string (3 letters, |x|=3)

The language I am interested in is $L=\{w∈\{a,b,c\}^*| w$ contains "$bac$" but not "$cab$"$\}$. I am thinking that the result will have the form $L=X_1X_2X_3$, where $X_1=\{w∈\{a,b,c\}^*| w$ does not ...
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Can a dfa return only the final state?

I am given an assignment to design a tiny arithmetic unit (from 0 to 15 inclusive) start with 0 and using a DFA. The operations are as follow: increment x+1 and if x+1 is larger than 15 then x+1 ...
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What kind of language does the following DFA accept?

can anyone please describe the language this FA accepts? thank you
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1answer
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Does this argument prove CFLs are not closed under union?

Context free languages are not closed under complementation. This follows from their property of non-closure under intersection: If CFLs were closed under complementation, then they must have also ...
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Prove that the following language is not regular: $\{0^i1^j : i \neq j\}$ [duplicate]

I was trying to approach this proof, after multiple reads and attempts I am getting nowhere. If someone could help me out that would be great. Should I use the pumping lemma, if so how show I start, ...
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Backwards and forwards automata languages compared with regular languages

Is every language accepted by a BAFDA regular? I am not even sure what the answer is. I tried thinking around canonical examples of non-regular languages (like $0^n1^n$ or $\{ww | w \in \{0,1\}^{*}\}$ ...
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Why are VFSMs not more commonly used?

For a job several years ago I worked with a team using technologies built around Virtual Finite State Machine models for system fault analysis and remediation. Since then, I've found it to be a ...
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1answer
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Are number of states in a NFA same as Pumping length?

So i was reading a post on Minimum pumping length of regular language where Yuval Filmus has proved that a pumping lemma might have lesser number of states than a minimal DFA. But What about NFA's? ...