Combine and Conquer

We present a general technique for dynamizing a class of problems whose underlying structure is a computation graph embedded in a tree. We associate values, called attributes, with the nodes, paths, and subtrees of our trees. Path attributes form a path attribute system, if they are maintained in constant time under path concatenation. Additionally, attributes form a tree attribute system if the tree attributes of the tail of a path \Pi are determined in constant time from the path attributes of \Pi. We also introduce a new data structure called a linear attribute grammar. An attribute grammar is a tree-based expression where the values a node are calculated from the values at the parent, siblings, and/or the children of . A linear attribute grammar, is an attribute grammar where all dependencies are linear. Our contributions can be summarized as follows. We provide a framework for maintaining attribute systems on trees in a fully dynamic environment. We show that given a ..