Efficient evaluation of circular attribute grammars

Abstract
We present efficient algorithms for exhaustive and incremental evaluation of circular attributes under any conditions that guarantee finite convergence. The algorithms are derived from those for noncircular attribute grammars by partitioning the underlying attribute dependency graph into its strongly connected components and by ordering the evaluations to follow a topological sort of the resulting directed acyclic graph. The algorithms are efficient in the sense that their worst-case running time is proportional to the cost of computing the fixed points of only those strongly connected components containing affected attributes or attributes directly dependent on affected attributes. When the attribute grammar is noncircular or the specific dependency graph under consideration is acyclic, both algorithms reduce to the standard optimal algorithms for noncircular attribute evaluation.

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