Finite Automate and Regular Sets

Question

I have a doubt in this that according to me the answer should be 6 as 5 states for modulo 5  + 1 dead state in starting as according to ques the string is starting from 1 so 0 production  will go to a dead state that's my assumption but behind the answer written is 7 states i m really confused how ?? Please help me what is its real answer

Comments

Here it;s.

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This is the DFA I m getting please correct my mistake i didn't understand how did u got 7.I m getting 6 states  what is wrong in mine and my final state is Q0 as 0 is the remainder i think that should be final state.Please tell my mistake in this DFA and thanks a lot all of you for your efforts :) 

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Strings in the language are

101,1010,1111,...............................etc.

Since its staring with "one" so when zero comes  it will be in trap state.

As well as see in your diagram 1010 is not accepting and many string multiple of 5 not accepting .

Answer 1

Number of States = 7

Comments

oh already answered.

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This is the DFA I m getting please correct my mistake i didn't understand how did u got 7.I m getting 6 states  what is wrong in mine and my final state is Q0 as 0 is the remainder i think that should be final state.Please tell my mistake in this DFA and thanks a lot all of you for your efforts :) 

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your dfa is wrong because in Question it  is clearly given that dfa should be start with 1. your Dfa  can accept ∈(Empty string) which is wrong. This is the main problem and cause of all other problems like your dfa can not accept string like {1010,10100 ,........} . According to your dfa {1010,10100 ,........} lead to dead state which is wrong .These string should be accept too.

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Thanks a lot everyone :)

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@leen pls explain Number of states in minimal finite automata that accepts all binary strings that starts with 101 and is divisible by 100. with shortcuts

Answer 2

Answer is 6 states . [excluding dead state( it didn’t ask for minimal DFA)]