Symbolic Boolean manipulation with ordered binary-decision diagrams
ACM Computing Surveys (CSUR)
Positive Boolean Functions as Multiheaded Clauses
Proceedings of the 17th International Conference on Logic Programming
The Def-inite Approach to Dependency Analysis
ESOP '01 Proceedings of the 10th European Symposium on Programming Languages and Systems
Efficient groundness analysis in Prolog
Theory and Practice of Logic Programming
Boolean equation solving as graph traversal
CATS '06 Proceedings of the 12th Computing: The Australasian Theroy Symposium - Volume 51
ACM Transactions on Programming Languages and Systems (TOPLAS)
Boolean equation solving as graph traversal
CATS '06 Proceedings of the Twelfth Computing: The Australasian Theory Symposium - Volume 51
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This note illustrates theoretical worst-case scenarios for groundness analyses obtained through abstract interpretation over the abstract domains of definite (Def) and positive (Pos) Boolean functions. For Def, an example is given for which any Def-based abstract interpretation for groundness analysis follows a chain which is exponential in the number of argument positions as well as in the number of clauses but sub-exponential in the size of the program. For Pos, we strengthen a previous result by illustrating an example for which any Pos-based abstract interpretation for groundness analysis follows a chain which is exponential in the size of the program. It remains an open problem to determine if the worst case for Def is really as bad as that for Pos.