How to conclude if logic circuit with feedback is combinational or sequential?
If you have combinatorial circuit with a feedback path from output to input then it's [by definition] an asynchronous sequential circuit. https://books.google.com/books?id=1QZEawDm9uAC&amp;pg=PA176

You have to make sure there's real state preserved there, i.e. the state saved actually affects the output(s). Otherwise it's a bogus/inconsequential "sequential" circuit, so really just combinatorial. In real life nobody would design that, but this being an academic exercise... you need to check.

You need to write (and simplify) the expression for z2 [if that's what I've circled below is called] and see if it actually depends on the old value of any inputs or not. Rafiquzzaman's textbook (to which I've linked) shows how to do this on an example (which actually has two state bits, but fewer inputs). Basically you treat old and new values as different variables (in this case z2) and apply k-maps etc. to simplify the expression to obtain a transition table for z2.



Regarding your equations, they seem wrong because there's no dependency of any on any [prior value of z]. Unless you've already simplified them... in which case, why are you still asking this question? But then your image so blurry I can't read practically any letters in it.