Reduced Ordered Binary Decision Diagram with Implied Literals: A New
  knowledge Compilation Approach
  Knowledge compilation is an approach to tackle the computational
intractability of general reasoning problems. According to this approach,
knowledge bases are converted off-line into a target compilation language which
is tractable for on-line querying. Reduced ordered binary decision diagram
(ROBDD) is one of the most influential target languages. We generalize ROBDD by
associating some implied literals in each node and the new language is called
reduced ordered binary decision diagram with implied literals (ROBDD-L). Then
we discuss a kind of subsets of ROBDD-L called ROBDD-i with precisely i implied
literals (0 \leq i \leq \infty). In particular, ROBDD-0 is isomorphic to ROBDD;
ROBDD-\infty requires that each node should be associated by the implied
literals as many as possible. We show that ROBDD-i has uniqueness over some
specific variables order, and ROBDD-\infty is the most succinct subset in
ROBDD-L and can meet most of the querying requirements involved in the
knowledge compilation map. Finally, we propose an ROBDD-i compilation algorithm
for any i and a ROBDD-\infty compilation algorithm. Based on them, we implement
a ROBDD-L package called BDDjLu and then get some conclusions from preliminary
experimental results: ROBDD-\infty is obviously smaller than ROBDD for all
benchmarks; ROBDD-\infty is smaller than the d-DNNF the benchmarks whose
compilation results are relatively small; it seems that it is better to
transform ROBDDs-\infty into FBDDs and ROBDDs rather than straight compile the
benchmarks.
