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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2512.00297 |
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| _version_ | 1866912978228477952 |
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| author | Wehar, Michael |
| author_facet | Wehar, Michael |
| contents | We reinvestigate known lower bounds for the Intersection Non-Emptiness Problem for Deterministic Finite Automata (DFA's). We first strengthen conditional time complexity lower bounds from T. Kasai and S. Iwata (1985) which showed that Intersection Non-Emptiness is not solvable more efficiently unless there exist more efficient algorithms for non-deterministic logarithmic space ($\texttt{NL}$). Next, we apply a recent breakthrough from R. Williams (2025) on the space efficient simulation of deterministic time to show an unconditional $Ω(\frac{n^2}{\log^3(n) \log\log^2(n)})$ time complexity lower bound for Intersection Non-Emptiness. Finally, we consider implications that would follow if Intersection Non-Emptiness for a fixed number of DFA's is computationally hard for a fixed polynomial time complexity class. These implications include $\texttt{PTIME} \subseteq \texttt{DSPACE}(n^c)$ for some $c \in \mathbb{N}$ and $\texttt{PSPACE} = \texttt{EXPTIME}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00297 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unconditional Time and Space Complexity Lower Bounds for Intersection Non-Emptiness Wehar, Michael Formal Languages and Automata Theory We reinvestigate known lower bounds for the Intersection Non-Emptiness Problem for Deterministic Finite Automata (DFA's). We first strengthen conditional time complexity lower bounds from T. Kasai and S. Iwata (1985) which showed that Intersection Non-Emptiness is not solvable more efficiently unless there exist more efficient algorithms for non-deterministic logarithmic space ($\texttt{NL}$). Next, we apply a recent breakthrough from R. Williams (2025) on the space efficient simulation of deterministic time to show an unconditional $Ω(\frac{n^2}{\log^3(n) \log\log^2(n)})$ time complexity lower bound for Intersection Non-Emptiness. Finally, we consider implications that would follow if Intersection Non-Emptiness for a fixed number of DFA's is computationally hard for a fixed polynomial time complexity class. These implications include $\texttt{PTIME} \subseteq \texttt{DSPACE}(n^c)$ for some $c \in \mathbb{N}$ and $\texttt{PSPACE} = \texttt{EXPTIME}$. |
| title | Unconditional Time and Space Complexity Lower Bounds for Intersection Non-Emptiness |
| topic | Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2512.00297 |