A switch-list representation (SLR) of a Boolean function is a compressed truth table representation of a Boolean function in which only (i) the function value of the first row in the truth table and (ii) a list of switches are stored. A switch is a Boolean vector whose function value differs from the value of the preceding Boolean vector in the truth table. The paper Čepek and Chromý (JAIR 2020) systematically studies the properties of SLRs and among other results gives polynomial-time algorithms for all standard queries investigated in the Knowledge Compilation Map introduced in Darwiche and Marquis (JAIR 2002). These queries include consistency check, validity check, clausal entailment check, implicant check, equivalence check, sentential entailment check, model counting, and model enumeration. The most difficult query supported in polynomial time by the smallest number of representation languages considered in the Knowledge Compilation Map is the sentential entailment check (of which the equivalence check is a special case). This query can be answered in polynomial time for SLRs, as shown in Čepek and Chromý (JAIR 2020). However, the query-answering algorithm is an indirect one: it first compiles both input SLRs into OBDDs (changing the order of variables for one of them if necessary) and then runs the sentential entailment check on the constructed OBDDs (both respecting the same order of variables) using an algorithm from the monograph by Wegener (2000). In this paper we present algorithms that answer both the equivalence and the sentential entailment query directly by manipulating the input SLRs (hence eliminating the compilation step into OBDD), which in both cases improves the time complexity of answering the query by a factor of n for input SLRs on n variables.

布尔函数的开关列表表示（SLR）是布尔函数的压缩真值表表示，其中仅存储（i）真值表中第一行的函数值和（ii）开关列表。开关是一个布尔向量，其函数值与真值表中前面的布尔向量的值不同。 Čepek 和 Chromý (JAIR 2020) 的论文系统地研究了 SLR 的属性，并在其他结果中给出了 Darwiche 和 Marquis (JAIR 2002) 引入的知识编译图中研究的所有标准查询的多项式时间算法。这些查询包括一致性检查、有效性检查、分句蕴涵检查、蕴含检查、等价性检查、句子蕴涵检查、模型计数和模型枚举。知识编译图中考虑的最少数量的表示语言在多项式时间内支持的最困难的查询是句子蕴含检查（其中等价检查是一个特例）。对于 SLR，此查询可以在多项式时间内得到回答，如 Čepek 和 Chromý (JAIR 2020) 中所示。然而，查询应答算法是一种间接算法：它首先将两个输入 SLR 编译为 OBDD（如有必要，更改其中一个的变量顺序），然​​后对构造的 OBDD 运行句子蕴含检查（两者都遵循相同的顺序）变量），使用 Wegener (2000) 专着中的算法。在本文中，我们提出了通过操纵输入 SLR 直接回答等价和句子蕴涵查询的算法（因此消除了 OBDD 的编译步骤），这在两种情况下都将回答查询的时间复杂度提高了 n 倍n 个变量的输入 SLR。