A worst case of circularity test algorithms for attribute grammars

Abstract

Although the circularity test problem for attribute grammars (AGs) has been proven to be intrinsically exponential, to date, a worst case for the existing circularity test algorithms has yet to be presented. This note presents a worst-case AG in which the number of incomparable dependency graphs induced at the root is exponential. The worst case can help to clarify the complexity of the problem.