We show a new connection between the clause space measure in tree-like resolution and the reversible pebble game on graphs. Using this connection, we provide several formula classes for which there is a logarithmic factor separation between the clause space complexity measure in tree-like and general resolution. We also provide upper bounds for tree-like resolution clause space in terms of general resolution clause and variable space. In particular, we show that for any formula F, its tree-like resolution clause space is upper bounded by space\((\pi)\)\((\log({\rm time}(\pi))\), where \(\pi\) is any general resolution refutation of F. This holds considering as space\((\pi)\) the clause space of the refutation as well as considering its variable space. For the concrete case of Tseitin formulas, we are able to improve this bound to the optimal bound space\((\pi)\log n\), where n is the number of vertices of the corresponding graph

我们展示了树状分辨率中的子句空间度量与图上的可逆卵石游戏之间的新联系。使用这种连接，我们提供了几个公式类，在树状和一般分辨率中的子句空间复杂性度量之间存在对数因子分离。我们还根据通用解析子句和变量空间提供了树状解析子句空间的上限。特别地，我们证明对于任何公式F，其树状解析子句空间的上限为空间\((\pi)\) \((\log({\rm time}(\pi))\)，其中\ (\pi \)是F的任何一般解析反驳。考虑到反驳的子句空间以及考虑其变量空间，这成立。对于 Tseitin 公式的具体情况，我们能够将这个边界改进为最佳边界空间\((\pi)\log n\)，其中n是相应图的顶点数