Bottom-Up Tree Acceptors

This paper deals with the formal derivation of an eecient tabulation algorithm for table-driven bottom-up tree acceptors. Bottom-up tree acceptors are based on a notion of match sets. First we derive a naive acceptance algorithm using dynamic computation of match sets. Tabulation of match sets leads to an eecient acceptance algorithm, but tables may be so large that they can not be generated due to lack of space. Introduction of a convenient equivalence relation on match sets reduces this eeect and improves the tabulation algorithm.