# What are the 5 tuples of a DFA?

Table of Contents

## What are the 5 tuples of a DFA?

DFA consists of 5 tuples {Q, Σ, q, F, δ}.

**How many states will be there for the minimum state DFA that accepts strings which ends with AA over the alphabet set a/b }?**

Ques-3: What is the minimum number of states in deterministic finite automata (DFA) for string starting with ba2 and ending with ‘a’ over alphabet {a, b}? Explanation: In the above DFA, minimum number of states required is six. Option (D) is correct.

### How many transitions can a DFA have?

A DFA has exactly one transition from every state on every symbol in the alphabet.

**What is NFA and DFA with Example?**

DFA stands for Deterministic Finite Automata. NFA stands for Nondeterministic Finite Automata. For each symbolic representation of the alphabet, there is only one state transition in DFA. No need to specify how does the NFA react according to some symbol. DFA cannot use Empty String transition.

## How are DFA processes strings?

Then first we shall check the transition δ (q0, S1) = q1 where q1 is the state where DFA reaches from q0 by input of S1 where DFA reaches from q0 by input. Then we apply δ(qi-1, Si) = qi for each i. If qn ∈ F then the input S1, S2, S3, ….. Sn is accepted otherwise the string is rejected.

**How many possible number of states in a minimal DFA that accept all the string must contain as lenth of string w/2 & string over Ʃ ={ a B?**

All strings starting with ‘n’ length substring will always require minimum (n+2) states in the DFA.

### How many number of states are there in a minimal DFA that accepts the strings?

So minimal DFA will have two states.

**Can DFA have missing transitions?**

My answer is an unequivocal: No. A deterministic finite automata does not need a transition from every state for every symbol. The meaning when δ(q,a) does not exist is simply that the DFA does not accept the input string.

## Can DFA have null transition?

DFA doesn’t have epsilon transitions. If it had it, it could transit from current state to other state without any input i.e. with nothing , not even {} or phi.

**How is DFA calculated?**

A DFA is represented by digraphs called state diagram. The vertices represent the states. The arcs labeled with an input alphabet show the transitions. The initial state is denoted by an empty single incoming arc….Example.

Present State | Next State for Input 0 | Next State for Input 1 |
---|---|---|

a | a | b |

b | c | a |

c | b | c |

### How do you minimize a DFA?

Minimization of DFA

- Step 1: Remove all the states that are unreachable from the initial state via any set of the transition of DFA.
- Step 2: Draw the transition table for all pair of states.
- Step 3: Now split the transition table into two tables T1 and T2.
- Step 4: Find similar rows from T1 such that:

**How do you determine if a DFA accepts a string?**

A string w is accepted by a DFA < Q , , q0 , , A > , if and only if *( q0 , w ) A . That is a string is accepted by a DFA if and only if the DFA starting at the initial state ends in an accepting state after reading the string.

## Can this DFA accept string?

DFA or Deterministic Finite Automata is a finite state machine which accepts a string(under some specific condition) if it reaches a final state, otherwise rejects it. In DFA, there is no concept of memory, therefore we have to check the string character by character, beginning with the 0th character.

**How many states does the DFA constructed for the set of all strings ending with ABA have?**

Design a DFA which accepts a language over the alphabets Σ = {a, b} such that L is the set of all strings starting with ‘aba’. All strings start with the substring “aba”. Therefore, length of substring = 3. Minimum number of states in the DFA = 3 + 2 = 5.

### What is the number of states required in minimal DFA to accept the strings of a regular that contains exactly two years and three 20 over the input alphabet AB?

As we need ( 3 * 3 + 1 ) = 10 states for 2 a’s and 2 b’s.

**Which one is the DFA minimization method?**

DFA minimization is usually done in three steps: remove dead and unreachable states (this will accelerate the following step), merge nondistinguishable states, optionally, re-create a single dead state (“sink” state) if the resulting DFA is required to be complete.