Test 1: typical mistake

Problem 2: to find x, y, and z, we need to find the
first pair of repeating states, i.e., the first instance
when a state repeats, then y is all the symbols in between
these two repetitions, etc.

Problem 3: there is only one starting state, but we
can have final states, so F = {c}, meaning F is a set
it is not true that F = c

Problem 4-5:

* forgetting the algorithms for union and intersection

* confusion on which states are final for union and which for

* not making the resulting automata deterministic: for some states
and some symbol, no arrow indicates where to go if we see this

Problem 6:

* forgetting that concatenation is, in general, not commutative: AB
is, in general, different from BA

* forgetting rules for union, concatenation, and Kleene star

Problem 7:

* forgetting to indicate, for some states and symbols, where we
should go if we see this symbol

* forgetting to indicate which states are final

* wrong use of algorithm: from one of the states, we go to the next
state and then we jump; we cannot directly go from one state to
another if this requires reading a sequence of two symbols

Problem 8-9:

* forgetting to add a new starting state and a new final

* the link to the new final state should be ONLY from
the old final state

* when you draw the new automaton with one state eliminated,
you need to draw all the arrows, with two exceptions:
from start state you only go out, to final state you only
go in; this means that it is necessary to also have an arrow
from the start state to the final state

* a,b over the arrow means a or b, i.e., it means the
union a U b; there is no comma in regular expressions,
and ab would mean concatenation not a or b

Problem 10:

* formulating the language wrong, L is NOT equal to
only sequences /\, mn, mmnn, etc., it also has mnmn etc.

* improvising instead of modifying the known proof

* remembering the pumping lemma wrong -- and clearly not having it
in your cheat sheet

* skipping parts of the proof, as a result of which
it is not clear where the conclusions come from

* weird notations like yi instead of i as a superscript,
mmmp instead of placing p below -- meaning that m is
repeated p time

* copying formulas with mistakes: e.g., xy...y is in L
z is missing, etc.