Verifying whether One-Tape Non-Deterministic Turing Machines Run in Time $Cn+D$

David Gajser

doi:10.1016/j.jcss.2019.08.004

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arXiv · 1312.0496

Verifying whether One-Tape Non-Deterministic Turing Machines Run in Time $Cn+D$

David Gajser

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Abstract

We discuss the following family of problems, parameterized by integers $C\geq 2$ and $D\geq 1$: Does a given one-tape non-deterministic $q$-state Turing machine make at most $Cn+D$ steps on all computations on all inputs of length $n$, for all $n$? Assuming a fixed tape and input alphabet, we show that these problems are co-NP-complete and we provide good non-deterministic and co-non-deterministic lower bounds. Specifically, these problems can not be solved in $o(q^{(C-1)/4})$ non-deterministic time by multi-tape Turing machines. We also show that the complements of these problems can be solved in $O(q^{C+2})$ non-deterministic time and not in $o(q^{(C-1)/2})$ non-deterministic time by multi-tape Turing machines.

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BibTeX RIS

David Gajser. 2013-12-02. Verifying whether One-Tape Non-Deterministic Turing Machines Run in Time $Cn+D$. https://doi.org/10.1016/j.jcss.2019.08.004

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