So I am going to find the occurrence of s in d. s = "infinite" and d = "ininfinintefinfinite " using finite automaton. The first step I need is to construct a state diagram of s. But I think I have problems on identifying the occurrence of the string patterns. I am so confused about this. If someone could explain a little bit on this topic to me, it'll be really helpful.
You should be able to use regular expressions to accomplish your goal. Every programming language I've seen has support for regular expressions and should make your task much easier. You can test your regexs here: https://regexr.com/ and find a reference sheet for different things. For your example, the regex /(infinite)/ should do the trick.