arXiv Open Access 2021

On formally undecidable propositions in nondeterministic languages

Martin Kolář
Lihat Sumber

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.

Topik & Kata Kunci

Penulis (1)

M

Martin Kolář

Format Sitasi

Kolář, M. (2021). On formally undecidable propositions in nondeterministic languages. https://arxiv.org/abs/2111.14807

Akses Cepat

Lihat di Sumber
Informasi Jurnal
Tahun Terbit
2021
Bahasa
en
Sumber Database
arXiv
Akses
Open Access ✓