Attribute Grammars and Automatic Complexity Analysis Attribute Grammars and Automatic Complexity Analysis Attribute Grammars and Automatic Complexity Analysis

Decomposable combinatorial structures have been well studied and a systematic manner for determining generating function equations is well known. Attribute grammars have enhanced the study of context-free grammars by giving meaning to constructions. Delest and F edou 2] showed that attribute grammars extend to combinatorial structures, with applications to random generation. In a similar way, we show attribute grammars can be deened for the family of decompo-sable structures and yield multivariate generating function equations. From there, averages and higher moments are easily accessible. This idea uniies previous approaches to the analysis of parameters of data-structures. Grammaires attribu ees et analyse automatique de complexit e R esum e : Les structures decomposables sont bien etudi ees, et une m ethode sys-tematique permettant d'obtenir des equations de fonctions g en eratrices est bien connue. Les grammaires attribu ees permettent de donner une signiication aux constructions des grammaires context-free. Delest et F edou ont montr e que les grammaires attribu ees s' etendent a certaines structures combinatoires, avec des applications a la g en eration al eatoire. De mani ere semblable, nous montrons que des grammaires attribu ees peuvent ^ etre deenies pour la famille des structures decom-posables, ce qui donne lieu a des equations de fonctions g en eratrices multivari ees. De ll a, moyennes et autres moments sont ais ement accessibles. Cett id ee uniie les approches pr ec edentes a l'analyse de param etres des structures de donn ees. Abstract. Decomposable combinatorial structures have been well studied and a systematic manner for determining generating function equations is well known. Attribute grammars have enhanced the study of context-free grammars by giving meaning to constructions. Delest and F edou 2] showed that attribute grammars extend to combinatorial structures, with applications to random generation. In a similar way, we show attribute grammars can be deened for the family of de-composable structures and yield multivariate generating function equations. From there, averages and higher moments are easily accessible. This idea uniies previous approaches to the analysis of parameters of data-structures.