Decomposable negation normal form
Journal of the ACM (JACM)
Compiling Knowledge into Decomposable Negation Normal Form
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Counting Models Using Connected Components
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
New compilation languages based on structured decomposability
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Journal of Artificial Intelligence Research
The good old Davis-Putnam procedure helps counting models
Journal of Artificial Intelligence Research
Compiling constraint networks into AND/OR multi-valued decision diagrams (AOMDDs)
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Using DPLL for efficient OBDD construction
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Hi-index | 0.00 |
A formal notion of a Boolean-function decomposition was introduced recently and used to provide lower bounds on various representations of Boolean functions, which are subsets of decomposable negation normal form (DNNF). This notion has introduced a fundamental optimization problem for DNNF representations, which calls for computing decompositions of minimal size for a given partition of the function variables. We consider the problem of computing optimal decompositions in this paper for general Boolean functions and those represented using CNFs. We introduce the notion of an interaction function, which characterizes the relationship between two sets of variables and can form the basis of obtaining such decompositions. We contrast the use of these functions to the current practice of computing decompositions, which is based on heuristic methods that can be viewed as using approximations of interaction functions. We show that current methods can lead to decompositions that are exponentially larger than optimal decompositions, pinpoint the specific reasons for this lack of optimality, and finally present empirical results that illustrate some characteristics of interaction functions in contrast to their approximations.