# 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.

1,745 questions
Filter by
Sorted by
Tagged with
60 views

### regular expression for $\{w\in \{a,b\}^*\mid |w|_a \mod 2 = 0\}\setminus \Sigma^*aab\Sigma^*$

The question asks to write down a regular expression $r$ indicating the language of all the words above $\Sigma = \{a, b\}$ , in which the number of $a$ is even and there is no sub-word $aab$ in them. ...
• 23
1 vote
67 views

### Resources on Moore and Mealy Machines

I was studying about Moore and Mealy machines but having hard time connecting with them because 1) they are different from typical normal machines.what is the need of "output" and 2) My text ...
• 57
54 views

### DFA that accepts strings ending with an even number of 1 in the last three characters ("000","110","101","011")

I need to design a binary DFA to accept strings where the last three characters read are either "000", "110", "101" or "011". My brutal solution is: I need ...
• 11
56 views

### Find a regular grammar that generates words with even number of a's and find a regular grammar that generates words with odd number of a's

I have a question about solution of these two exercises: Find a regular grammar that generates words with even number of a's and find a regular grammar that generates words with odd number of a's. ...
• 1
30 views

### Create NFA where |w|_a is divisible by 2 or |w|_b is divisible by 3

I have to create an NFA $\mathcal{A}$ that accepts the language $L = \{w \in \Sigma^* \ | \ |w|_a \ \text{is divisible by 2 or} \ |w|_b \ \text{is divisible by 3} \}$ So the NFA only accepts words ...
• 21
1 vote
60 views

### How to show L is non-regular without pumping lemma?

$L=\{(ab)^n : n\text{ is a natural number apart from }6\}$, I want to show L is non-regular by finding an infinite set of L-distinguishable words. Could you help me?
• 23
14 views

### Hardwiring input in DFAs and PDAs

A Turing Machine can be converted into a Turing Machine that has a specific input coded into it's description. This Turing Machine can then be run on empty input. Can we do the same for PDAs or DFAs? ...
• 191
69 views
+100

### Constructing worst case for L* by D.Angluin

I'm working on constructing deterministic finite automata (DFAs) with a specific learning complexity when using the L* algorithm developed by Dana Angluin. My goal is to create a DFA of size ( n ) ...
161 views

### Difference between product automaton vs. NFA with epsilon transitions

Let $L_1, L_2$ be regular languages. You can proof with a product automaton that $L_1\cup L_2$ is also regular. But you can also construct a NFA. Since $L_1, L_2$ are regular, they also have an NFA ...
261 views

### Pumping Lemma Applied to 3 Variables

Prove That the Language $L_1 = \{0^i1^j0^k | i < j\ or\ i > k\}$ is not regular using the pumping lemma. I am not sure how to begin with this I ended up using the string: $0^p1^{p+1}0^{p+1}$ S = ...
• 23
1 vote
52 views

### Provide a 2-state DFA for L={a}∗{b}∗ , the set of words of the form aa⋯abb⋯b

I'm kinda confused on how to construct this DFA. I'm trying but keep running into the problem of reading an a after the b's or what to do if starting with a 'b'.
34 views

### Trouble proving this is regular

I'm taking an automata class and one of the examples is showing this is regular. My initial thought was to make a DFA to show it is but i'm a bit confused on what a DFA with a standard 5 tuple would ...
17 views

### Theory of computation - computer science

For each of the following languages ​​construct a non-deterministic finite automaton that recognizes it. In any case show the state diagram of the automaton (only). (a) Four-state nondeterministic ...
1 vote
57 views

### Why can't we prove closure under concatenation using DFA?

I can't understand why do we have to use NFA to prove that concatenation operation is closed. According to sisper's book it says that we can't determine where to split the string, i.e. where to ...
• 57
30 views

### Create regular expression from finite automata

Hello, I am trying to grasp the concept of regular expressions on FAs Am I right in saying that the regular expression for the first DFA is (ab)*? As for others, ...
858 views

### Converting Regex to DFA

People I know said that converting a Regex to DFA is just a "matter of judgement" (I do not believe them, there has to be a more systematic approach). Is there a simple/intuitive, yet ...
37 views

### What does the language of DFA of LR itemsets represent?

As we know, if we want to make a $LR(0)$ (say) parsing table for a context free grammar (CFG), we prepare the $LR(0)$ itemsets with $.$ (dot) in RHS of the CFG production. With this $.$ we keep track ...
68 views

### NFA for the language that accepts binary strings ending with 00

This is the question: 1.7. Give state diagrams of NFAs with the specified number of states recognizing each of the following languages. In all parts, the alphabet is {0,1}. a. The language {w| w ...
• 3
56 views

### How to work thompson's construction algorithm?

Could someone explain to me, through an example, how the McNaughton–Yamada–Thompson algorithm works in a way that I can understand? Thank you in advance for your helpful response!
41 views

### Is this correct Context free grammar(CFG) for these two languages?

Question 1: L = { 0^n 1^n | n > 0 } My answer = S -> 0 S 1 | 10 Question 2: L = { 101^n0^2n | n > 0 } My answer = S -> 101 S 00 | 100 Can anyone correct this if there is any issue with ...
1 vote
28 views

### In regular language inference, how is the observation table kept consistent?

I am trying to understand the background literature on regular language inference in the TTT paper ("The TTT Algorithm: A Redundancy-Free Approach to Active Automata Learning" by Isberner, ...
1 vote
110 views

### How to construct complement of NFA universality?

Given an input NFA, can one construct an NFA that is universal (that is, accepts all its inputs) if and only if, the input NFA isn't universal? I tried to use the fact that NFA-universality is PSPACE-...
• 123
100 views

### Applications of ω-automaton in engineering

Finite automaton is a well-known topic which finds applications in software engineering (e.g. pattern matching or regular expressions in general). ω-automaton are another kind of automaton, defined ...
• 231
50 views

### Determining the language of a DFA

I've tried quite a large amount of examples, starting from 1 bit all the way up to 5 bits yet I couldn't put my finger on any recurring pattern of words that are accepted. the DFA is as such: The ...
• 345
1 vote
249 views

### How to build a deterministic or non deterministic finite automat for a language

$L_1$ and $L_2$ are two languages that have a finite deterministic automaton. $Σ = \{0,1\}$ for the two languages. Let $L=\{x∈L_1\mid \text{there exists } y∈L_2,\text{such that } \#_0(x)=\#_0(y)\}$, ...
• 11
62 views

### Proving that the intersection of two languages is regular or not?

Let $B$ and $C$ be two languages on $A = \{a,b\}$: $B = \{ w \mid w \text{ has the same number of }a\text{ and }b\text{ symbols}\}$ $C = \{ a^n b^m \mid n,m \ge 0\}$ Describe $B \cap C$ and determine ...
• 63
55 views

### Intersection of a regular and a non-regular language can give a non-regular language?

Determine two languages L and L1 on the alphabet {a,b} with regular L, L∩L1 is non-regular and L1 does not contain L. I came up with this solution: L = { w | w ends with the string aba} L1 = {w | w = ...
• 63
60 views

### Can the intersection of 2 non-regular languages ​be a regular and infinite language?

The outline of the exercise is this: Describe two non-regular L1 and L2 languages on A = {a,b} such that L1∩L2 is infinite and regular. The proposed solution to this exercise is: L1 = {a^n b^n | n >...
• 63
38 views

### Proving a language is not regular using Pumping Lemma

So I am given the language qr where q is any combination of a's and b's. r is then the reverse of whatever q is. For example, abba is in the language because we can make a q = ab and r = ba I have to ...
1 vote
12 views

### Is there a symbol in FA/FSM for everything else

I remember in a Computability Theory class building a state machine for an assignment that required many 'go-back' transitions on $\Sigma - symbols$ for all symbols not already handled. This was very ...
• 111
37 views

### Can someone explain the following NFA?

I'm learning NFA and the following question is confusing me. Can Someone explain the answer. I have a feeling that it might be wrong. Thank you!
235 views

### Create DFA such that every substring of w of length 3 contains two or three 0's with w={0,1}

I am attempting to draw the DFA of this problem but I'm kind of stuck. In another post I saw that the DFA should have 10 states. I'm finding it hard to even understand the question, is the input to ...
50 views

### 1 way 2 stack and 2 way 2 stack Pushdown Accepters that accepts $L=\{a^{(n^2)} \mid n \geq 1\}$

Using a 1 way 2 stack, and a 2 way 2 stack PDA, I want to check if the length of an input string is strictly a perfect square number. How can I do this in both approaches?
62 views

### Why does lexer has O(n) time complexity?

According to my CS knowledge so far, a lexer uses DFA(which takes linear time) for 'each' token type to find the next token, so in the worst case, it should try 'all possible' token types of a ...
102 views

### How to find prefixes and suffixes for infinite languages? (Automata)

L= {abc} prefix = {epsilon,a,ab,abc} suffix = {epsilon,c,bc,abc} It's easy to find suffixes and prefixes for finite Regular languages. But what will be the ...
132 views

### Turing machine for a^n b^m c^n d^m

The state diagram for the initial part of this turing machine given as: Here, we are basically traversing through the input tape, changing occurence of 'a' to X1, and 'c' to X2. After that we go back ...
• 101
33 views

### What is the minimum length word accepted by the product of these simple loop automata?

Let $A_{n} = (aa|aaa|aaaa|\dots |a^{n-2})(a^{n})^*$ where $n \geq 4$ is some natural,and $A_2 = (a^2)^*, A_3 = (a^3)^*$. Clearly every transition is thus labeled by an $a$. From now on let $A_n$ ...
95 views

### What is the Minimum length of a string that is accepted by a DFA that shows that the language accepted by that DFA is infinite?

What is the minimum length of a string that is accepted by a DFA, shows that the language accepted by that DFA is infinite? I checked this post How to determine if an automata (DFA) accepts an ...
100 views

### Construct a regular grammar that produces all possible strings of $\Sigma = \{a,b\}$ that do not contain substring 'abba'

I'm really stuck here and do not know what to do. So far, I've constructed a DFA and a regular expression that produces the aforementioned set of strings. Namely, the DFA looks like: After a lot of ...
1 vote
69 views

### DFA for even concatenation of strings from a language

If I have a deterministic finite automaton (DFA) with a language $W$, and I need to create another DFA that returns all the strings that are a concatenation of an even number of strings in $W$, how ...
50 views

### After converting a CFG to a PDA, what is an example input string to the PDA?

For example, the following CFG: S$\rightarrow$aSb|$\epsilon$ A valid string within the language described by the CFG would be, e.g., "aabb". The converted PDA has the following form: The ...
• 111
44 views

### Binary combinatorics with rank

I am looking at finding acceptable binary values with maximum 2 consecutive 1s and 0s, from a range of maximum 6 bits (2^6 values). Also, I want to rank and unrank these subset of values (in ...
• 23
39 views

### DFA for "K" bit value with max "n" consecutive "0"s and "1"s

I had posted earlier a question regarding ranking max "n" consecutive "0"s and "1"s in a "K"-bit string - Order in a subset I got clarification regarding how ...
• 23
169 views

### Minimum number of states in a DFA

Consider the language L given by the regular expression (a + b )*b(a + b) over the alphabet {a, b} . The smallest number of states needed in a deterministic finite-state automaton (DFA) accepting L is ...
57 views

### How to convert a NFA to alternating finite automata AFA?

I am trying to construct an AFA from a NFA, how do I know if a state of NFA becoms existential or universal in the AFA?
• 1
72 views

### Question about remainder in automata construction that checks divisibility

I'm trying to understand de construction of a DFA from the book "Introduction to Automata Theory, Languages, and Computation by John Hopcroft and Jeffrey Ullman 1st ed" It says: Where it ...
• 101
94 views

### Is the set of all DFAs countable?

Let $\Sigma$ be a finite nonempty alphabet. Is the set of all DFAs over $\Sigma$ countable? I know the set of all regular languages is countable, however, it is impossible to build an injection from ...
41 views

Let us assume, we have a FSM (to be precise, an epsilon-NFA) in which I've got redundant structures. I am looking for a framework that allows to factor out the redundant part into some kind of ...
• 101
76 views

### Translating non-deterministic finite automata with counters to deterministic ones

I know there are algorithms for translating regular NFAs into their corresponding DFAs. Can these algorithms be applied to automata that employ transitions involving counters in a straightforward way, ...
• 141