A very sharp threshold for first order logic distinguishability of random graphs
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866911053023019008 |
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| author | Benjamini, Itai Zhukovskii, Maksim |
| author_facet | Benjamini, Itai Zhukovskii, Maksim |
| contents | In this paper we find an integer $h=h(n)$ such that the minimum number of variables of a first order sentence that distinguishes between two independent uniformly distributed random graphs of size $n$ with the asymptotically largest possible probability $\frac{1}{4}-o(1)$ belongs to $\{h,h+1,h+2,h+3\}$. We also prove that the minimum (random) $k$ such that two independent random graphs are distinguishable by a first order sentence with $k$ variables belongs to $\{h,h+1,h+2\}$ with probability $1-o(1)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2207_11593 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A very sharp threshold for first order logic distinguishability of random graphs Benjamini, Itai Zhukovskii, Maksim Combinatorics Logic in Computer Science Logic Probability In this paper we find an integer $h=h(n)$ such that the minimum number of variables of a first order sentence that distinguishes between two independent uniformly distributed random graphs of size $n$ with the asymptotically largest possible probability $\frac{1}{4}-o(1)$ belongs to $\{h,h+1,h+2,h+3\}$. We also prove that the minimum (random) $k$ such that two independent random graphs are distinguishable by a first order sentence with $k$ variables belongs to $\{h,h+1,h+2\}$ with probability $1-o(1)$. |
| title | A very sharp threshold for first order logic distinguishability of random graphs |
| topic | Combinatorics Logic in Computer Science Logic Probability |
| url | https://arxiv.org/abs/2207.11593 |