# Solving Regular Tree Grammar Based Constraints

Yanhong A. Liu, Ning Li, and Scott D. Stoller

This paper describes the precise specification, design, analysis,
implementation, and measurements of an efficient algorithm for
solving regular tree grammar based constraints. The particular
constraints are for dead-code elimination on recursive data, but
the method used for the algorithm design and complexity analysis
is general and applies to other program analysis problems as well.
The method is centered around Paige's finite differencing, i.e.,
computing expensive set expressions incrementally, and allows the
algorithm to be derived and analyzed formally and implemented
easily. We study higher-level transformations that make the
derived algorithm concise and allow its complexity to be analyzed
accurately. Although a rough analysis shows that the worst-case
time complexity is cubic in program size, an accurate analysis
shows that it is linear in the number of live program points and
in other parameters that are typically smaller in practice. Our
implementation ranges from two to ten times as fast as a previous
implementation of an informally designed algorithm.
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