Reduced Ordered Binary Decision Diagram with Implied Literals: A New knowledge Compilation Approach

TL;DR

This paper introduces ROBDD-L, a generalized form of ROBDD with implied literals, which improves knowledge compilation efficiency and compactness, demonstrated through algorithms and preliminary experiments.

Contribution

It proposes a new knowledge compilation language, ROBDD-L, with associated algorithms, and shows its advantages over traditional ROBDDs and other formats in size and query capability.

Findings

ROBDD- is smaller than ROBDD for all benchmarks.

ROBDD- outperforms d-DNNF in size for certain benchmarks.

Transforming ROBDD- into FBDDs may be more effective than direct compilation.

Abstract

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.