| Autor: |
Wang, Kexu, Feng, Shiguang, Zhao, Xishun |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Logical Methods in Computer Science, Volume 19, Issue 3 (July 14, 2023) lmcs:9812 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.46298/lmcs-19(3:6)2023 |
| Popis: |
We study the expressive power and complexity of second-order revised Krom logic (SO-KROM$^{r}$). On ordered finite structures, we show that its existential fragment $\Sigma^1_1$-KROM$^r$ equals $\Sigma^1_1$-KROM, and captures NL. On all finite structures, for $k\geq 1$, we show that $\Sigma^1_{k}$ equals $\Sigma^1_{k+1}$-KROM$^r$ if $k$ is even, and $\Pi^1_{k}$ equals $\Pi^1_{k+1}$-KROM$^r$ if $k$ is odd. The result gives an alternative logic to capture the polynomial hierarchy. We also introduce an extended version of second-order Krom logic (SO-EKROM). On ordered finite structures, we prove that SO-EKROM collapses to $\Pi^{1}_{2}$-EKROM and equals $\Pi^1_1$. Both SO-EKROM and $\Pi^{1}_{2}$-EKROM capture co-NP on ordered finite structures. |
| Databáze: |
arXiv |
| Externí odkaz: |
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