Evaluation of Mistakes in Computablity Written Tests

This page describes the penalties applied to specific mistakes in written tests. For serious errors, these can bring the score of a whole exercise below zero: in that case, not doing the exercise would have awarded a better score.

Instant failure: a single occurence of these mistakes causes the failure of the whole test -- even if the rest is perfect.

  1. Stating that, since the hypothesis of a known theorem does not hold, the thesis does not hold as well. Notable examples:
  2. Stating that a set is recursive but not recursively enumerable.
  3. Stating that the set of natural numbers, even naturals, odd naturals, or primes is a finite set. Similarly for other infinite ``well-known'' sets.
  4. 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.

Negative points: these mistakes award negative points, typically making the whole exercise detrimental to the overall score.

  1. Writing a formula which does not respect ``types'', i.e. it mixes functions/sets/programs/natural numbers in a meaningless way. Examples:
  2. Arbitrarily choosing the value of a universally/existentially quantified variable. Examples:
  3. Defining functions/sets through formulae involving undefined variables.
  4. Using Rice-Shapiro without being clear about which direction you are using.
  5. Using logic in a remarkably creative way.

Answer invalidation: forcefully misreading a question so that it becomes trivial will award zero points for that question.

No penalty: small mistakes which do not invalidate the overall reasoning do not award negative points.

  1. Misreading a constant in the question which do not affect the essence of the exercise.
  2. Miscalculating an arithmetic expression without affecting the overall reasoning.
  3. Avoiding the simple solution and providing a much longer, but correct, alternative answer.

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