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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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Is the following extension of finite state automata studied?

Consider a finite state machine as usual, but every transition, it can also update an integer counter by adding or subtracting a number. Say, a transition function of the form $\delta(q,a) = (p,k)$ moves to the new state $p$, and add $k$ to the…
Chao Xu
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Understanding definition of epsilon closure and finite automata states

I am going through the book , introduction to compiler design , by Torben Ægidius Mogensen. It provides the following definition of an epsilon closure : Given a set M of NFA states, we define $\ \epsilon $-closure($\ M $) to be the least (in terms…
Eddie Dorphy
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Proof that for 2n nodes of +1 and -1 position doesn't count

I'm having a hard time understanding how to solve this problem for my Computer Science 101 class. On a circle there are $2n$ nodes. $n$ out of these hold -1 power and $n$ hold +1 power. Say we play a game where we randomly start from a node and move…
Tita
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Determine the number of reachable states in a subset construction?

Is there a polynomial time algorithm to determine the number of reachable states in the subset construction of a NFA to a DFA without having to construct the entire DFA?
ICTOAUN
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Minimum number of states in the DFA

I am trying to solve following problem but unable to solve this. Can anyone tell me how to approach this kind of problems where it is not easy to make DFA. The minimum number of states required to construct a DFA that recognizes the language of…
Mr. Sigma.
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n-state DFA that requires n-2 steps to check equivalence

We have a DFA $A = (Q,\Sigma, \delta, q_0, F)$. States $p, q$ $\in Q$ are equivalent, $p \sim q$ if $ \forall w \in \Sigma ^ \ast$ $ \delta^*(p,w) \in F \iff \delta^*(q,w) \in F$ States $p,q$ are equivalent after $i$ steps, $p \sim ^i q$, if $…
mathew7k5b
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Prove that every substring closed language L ⊆ {0, 1}* is regular

For $x,y \in \{0,1\}^*$ a language $L ⊆ \{0, 1\}^*$ is called substring closed, if $y \in L$ and $x \preceq y$ ($x$ substring of $y$) implies $x \in L$. I want to prove that every substring closed language $L ⊆ \{0, 1\}^*$ is regular. Is it enough…
MR.-c
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Are Epsilon-NFAs a way to make designing NFAs easier?

It seems that their purpose is in making designing certain NFAs less onerous? Does this mean that no automata that are implemented have Epsilon-transitions, and that they are kind of a mathematical conceit we adopt for our own ease of design? I'm…
Chris T
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Need help trying to figure out DFA

Can anyone please help me try to understand what will the state diagram look like for this question: Let $L = \{x_0y_0z_0x_1y_1z_1\ldots x_{n-1}y_{n-1}z_{n-1} \mid \exists n,x,y,z \, x+y=z \land x=\sum_{j=0}^{n-1} x_j2^j \land y=\sum_{j=0}^{n-1}…
El Dj
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Are DFAs unique?

For a given regular is expression, once we construct a deterministic finite automaton: is that automaton unique for that expression? In a sense, that no other DFA (different number of vertices or transitions) can be constructed from that same…
monolith937
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Where Can I Find DFA Practice?

Where can I find a web site or book where I can practice drawing DFAs from a language like " {w| w has at least three a’s and at least two b’s} ". It will be important to have access to the answer so as to check myself. I need the practice.
Delete My Account
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Can every state in a DFA be an accepting state?

I know that we can have 0 accepting states in a DFA, it would just recognize the empty language. What about the case of all states being accepting? Would that mean it would recognize all of the strings in the DFA's particular alphabet? Thanks
Enis
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What does an input string of epsilon mean?

I am currently reading Introduction to the Theory of Computation (Sipser), and after introducing epsilon labeled transition arrows, the book shows the following NFA: I was following it until I read the following : Practice with it to satisfy…
jcw
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Brzozowski's algorithm for Kleene star NFA

I have some troubles in understanding of the Brzozowski's algorithm for NFA to minimized DFA transformation. Or maybe I'm doing a mistake in the NFA to DFA transformation steps. The Algorithm, as described in Wikipedia, is as follows: Reverse the…
Ilya Lakhin
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Hopcroft's minimization algorithm produces an incorrect result for a particular regular expression

I'm writing a DFA minimizer using Hopcroft's algorithm. While testing some regular expressions, I came out with an issue in the algorithm's output relative to two particular regular expressions: a(b|c)* a(b|c*) P.S.: the assumption is that both…
Ψray
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