unsolvability
Noun
Meaning
unsolvability (countable and uncountable, plural unsolvabilities)
The property of being unsolvable.
Synonyms
Antonyms
Hypernyms
Examples
As a result of its unsolvability, several other problems in combinatorial group theory have been shown to be unsolvable as well.
For first-order syntactical unification, Martelli and Montanari citation gave an algorithm that reports unsolvability or computes a complete and minimal singleton substitution set containing the so-called most general unifier.
The first results about unsolvability, obtained independently by Church and Turing in 1936, showed that the Entscheidungsproblem is algorithmically unsolvable.
The 'main idea' might have either been his analysis of computation or his realization that there was a universal machine, and so a diagonal argument to prove unsolvability.
For example, the conventional proof of the unsolvability of the halting problem is essentially a diagonal argument.
The algorithmic unsolvability of the problem was proved by Yuri Matiyasevich in 1970 (Davis 1973).