DPLL algorithm for solving the Boolean satisfiability problem (SAT) can be represented in the form of a procedure that, using heuristics $A$ and $B$, select the variable $x$ from the input formula $\varphi$ and the value $b$ and runs recursively on the formulas $\varphi[x := b]$ and $\varphi[x := 1 - b]$. Exponential lower bounds on the running time of DPLL algorithms on unsatisfiable formulas follow from the lower bounds for tree-like resolution proofs. Lower bounds on satisfiable formulas are also known for some classes of DPLL algorithms such as "myopic" and "drunken" algorithms. All lower bounds are made for the classes of DPLL algorithms that limit heuristics access to the formula. In this paper we consider DPLL algorithms with heuristics that have unlimited access to the formula but use small memory. We show that for any pair of heuristics with small memory there exists a family of satisfiable formulas $\Phi_n$ such that a DPLL algorithm that uses these heuristics runs in exponential time on the formulas $\Phi_n$.

翻译：DPLL 解决布利安可食性问题( SAT) 的 DPLL 算法可以表现为一种程序, 程序的形式是, 使用树类解析证据的下限, 从输入公式中选择变量 $A$和 $B$, 从输入公式中选择变量 $x$x$, 和 $B$, 并反复运行公式中的 DPLL DPL 算法 [x: = b] 美元 和 $\ varphi [x: = 1 - b]$. 。 在本文中, DPLLL 算法运行时间的下限可以代表无法满足的公式, 但使用少量的记忆。 对于具有小记忆的超值公式中的超值公式, DPLLV 和 drungkn 运算法的下限范围都由DPLLV 格式组成。 我们向任何具有小记忆的超值的超值公式, DPLLLLL 将使用这种动态公式的 。