I need to design an FSM sequence detector that activates when it detects the sequences 01011 and 00101. The problem is that I don't know how, for example, when state s3 receives the value 0 and reaches 010, to make s3 transition to 001 if it receives a 1. This is the design I made:



I need someone to help me not to make the complete diagram but to give me a brief textual summary of how the transitions should be depending on whether they receive 1 or 0."

 

A big piece that is missing is whether your machine is looking for either of those two sequences anywhere within a larger sequence, or if it is only looking for them to be at the start of a sequence.

For example:

What is the sequence provided were

1010100010110010

What should the output be after each bit in that sequence is read?

 

That whole check can be done in basic, using "IF" statements, if you have a few seconds available.
It seems like what you are seeking can be done with a "correlation sensor" which is a custom IC that I came across many years ago.