Previous work on Dynamic Complexity has established that there exist dynamic constant-time parallel algorithms for regular tree languages and context-free languages under label or symbol changes. However, these algorithms were not developed with the goal to minimise work (or, equivalently, the number of processors). In fact, their inspection yields the work bounds $O(n^2)$ and $O(n^7)$ per change operation, respectively. In this paper, dynamic algorithms for regular tree languages are proposed that generalise the previous algorithms in that they allow unbounded node rank and leaf insertions, while improving the work bound from $O(n^2)$ to $O(n^{\epsilon})$, for arbitrary $\epsilon > 0$. For context-free languages, algorithms with better work bounds (compared with $O(n^7)$) for restricted classes are proposed: for every $\epsilon > 0$ there are such algorithms for deterministic context-free languages with work bound $O(n^{3+\epsilon})$ and for visibly pushdown languages with work bound $O(n^{2+\epsilon})$.

翻译：先前的动态复杂度研究已表明，在标签或符号变更条件下，存在针对正则树语言和上下文无关语言的动态常数时间并行算法。然而，这些算法在设计时并未以最小化工作（即处理器数量）为目标。事实上，通过分析可知，每次变更操作的工作复杂度分别达到$O(n^2)$和$O(n^7)$。本文提出针对正则树语言的动态算法，在以下方面推广了先前工作：允许无界节点秩和叶节点插入，同时将工作复杂度从$O(n^2)$改进至$O(n^{\epsilon})$（对任意$\epsilon > 0$成立）。对于上下文无关语言，本文提出在受限类别中具有更优工作复杂度（相对于$O(n^7)$）的算法：对任意$\epsilon > 0$，可构造工作复杂度为$O(n^{3+\epsilon})$的确定型上下文无关语言算法，以及工作复杂度为$O(n^{2+\epsilon})$的可视化下推语言算法。