On formally undecidable propositions in nondeterministic languages
Abstract
Any class of languages $\mathbf{L}$ accepted in time $\mathbf{T}$ has a counterpart $\mathbf{NL}$ accepted in nondeterministic time $\mathbf{NT}$. It follows from the definition of nondeterministic languages that $\mathbf{L} \subseteq \mathbf{NL}$. This work shows that every sufficiently powerful language in $\mathbf{L}$ contains a string corresponding to Gödel's undecidable proposition, but this string is not contained in its nondeterministic counterpart. This inconsistency in the definition of nondeterministic languages shows that certain questions regarding nondeterministic time complexity equivalences are irrevocably illposed.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2111.14807
 Bibcode:
 2021arXiv211114807K
 Keywords:

 Computer Science  Formal Languages and Automata Theory;
 Computer Science  Computational Complexity;
 68Q15;
 03D35
 EPrint:
 4 pages