Similar to the satisfiability (SAT) problem, which can be seen to be the archetypical problem for NP, the quantified Boolean formula problem (QBF) is the archetypical problem for PSPACE. Recently, Atserias and Oliva (2014) showed that, unlike for SAT, many of the well-known decompositional parameters (such as treewidth and pathwidth) do not allow efficient algorithms for QBF. The main reason for this seems to be the lack of awareness of these parameters towards the dependencies between variables of a QBF formula. In this paper we extend the ordinary pathwidth to the QBF-setting by introducing prefix pathwidth, which takes into account the dependencies between variables in a QBF, and show that it leads to an efficient algorithm for QBF. We hope that our approach will help to initiate the study of novel tailor-made decompositional parameters for QBF and thereby help to lift the success of these decompositional parameters from SAT to QBF.

与可满足性（SAT）问题（可以看作是NP的原型问题）相似，量化布尔公式问题（QBF）是PSPACE的原型问题。最近，Atserias和Oliva（2014）表明，与SAT不同，许多众所周知的分解参数（例如树宽和路径宽）不允许有效的QBF算法。造成这种情况的主要原因似乎是缺乏对QBF公式变量之间的依存关系的这些参数的了解。在本文中，我们通过引入前缀路径宽度将普通路径宽度扩展到QBF设置，该前缀路径宽度考虑了QBF中变量之间的相关性，并表明这导致了一种有效的QBF算法。