arXiv
Open Access
2021
On formally undecidable propositions in nondeterministic languages
Martin Kolář
Abstrak
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 ill-posed.
Penulis (1)
M
Martin Kolář
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2021
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓