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