This page lists some specific significant mistakes which I found to be common in answers to the written tests. Since some of them are way too common, I am putting some penalties on them. I'd rather prefer a missing answer than one carrying one of these mistakes.

*Critical Mistakes*: these are likely to cause the rejection of
your whole answer sheet, no matter how good the other answers may be.

- Stating that, since the hypothesis of a known theorem does not hold,
the thesis does not hold as well. Notable examples of this mistake:
- Using Rice's theorem to prove that a set is recursive.
- Using the Rice-Shapiro theorem to prove that a set is recursively enumerable.

- Stating that a set is recursive but not recursively enumerable.
- Stating that the set of natural numbers, even naturals, odd naturals, or primes is a finite set. Similarly for other infinite ``well-known'' sets.
- Stating that the Kleene's set K is recursive; or that K is not recursively enumerable; or that the complement of K is recursively enumerable.

*Major Mistakes*: these are likely to award a negative score. Unless
the other answers are good to compensate, your overall score might fall
under the threshold to pass the written test.

- Using Rice-Shapiro without being clear about which direction you are using.
- Writing a formula which does not respect ``types'', i.e. it mixes
functions/sets/programs/natural numbers in a meaningless way. Examples:
- Writing ``x belongs to y'' when y is not a set (but e.g. is a function, a program, or a natural number)
- Writing ``x belongs to A'' when A is a set of functions/natural numbers/programs, while x is not a function/natural number/program (respectively).
- Writing ``f(x)'' when f is not a function.
- Writing ``x + y'' when x and y are not numbers.
- Stating that a function is (not) recursively enumerable. (whatever that would mean)
- (not exhaustive list)

- Arbitrarily choosing the value of a variable
(e.g. ``I pick x=5, hence p(5) holds'')
when you can not
(e.g. you applied a theorem stating that ``
*for some*x, p(x) holds'')

*Wishful Reading Mistakes*: misreading a question so that it
becomes trivial will award zero points. Do not waste your time: if you
do not know the answer, skip the question instead.

*Standard Mistakes*: these will not award negative points,
but award no positive points, either.

- Rewriting a logical formula, arithmetic formula, set formula in a non-equivalent way. E.g. x*y+4 = x*(y+4)
- Simple mistakes e.g. ``4+3=8'' which do not make the exercise trivial.

*Infelicities*: these, technically speaking, are not mistakes,
but can be described as ``taking the stairs instead of the lift at the
Empire State Building''.
There is no penalty for these, but for the fact that you wasted your time
during the test.

- Proving a set to be non recursively enumerable, and then proving (from scratch) that it is non recursive.

Roberto Zunino, 2010