Augmenting Ordered Binary Decision Diagrams with Conjunctive Decomposition

24 Oct 2014  ·  Yong Lai, Dayou Liu, Minghao Yin ·

This paper augments OBDD with conjunctive decomposition to propose a generalization called OBDD[$\wedge$]. By imposing reducedness and the finest $\wedge$-decomposition bounded by integer $i$ ($\wedge_{\widehat{i}}$-decomposition) on OBDD[$\wedge$], we identify a family of canonical languages called ROBDD[$\wedge_{\widehat{i}}$], where ROBDD[$\wedge_{\widehat{0}}$] is equivalent to ROBDD... We show that the succinctness of ROBDD[$\wedge_{\widehat{i}}$] is strictly increasing when $i$ increases. We introduce a new time-efficiency criterion called rapidity which reflects that exponential operations may be preferable if the language can be exponentially more succinct, and show that: the rapidity of each operation on ROBDD[$\wedge_{\widehat{i}}$] is increasing when $i$ increases; particularly, the rapidity of some operations (e.g., conjoining) is strictly increasing. Finally, our empirical results show that: a) the size of ROBDD[$\wedge_{\widehat{i}}$] is normally not larger than that of the equivalent \ROBDDC{\widehat{i+1}}; b) conjoining two ROBDD[$\wedge_{\widehat{1}}$]s is more efficient than conjoining two ROBDD[$\wedge_{\widehat{0}}$]s in most cases, where the former is NP-hard but the latter is in P; and c) the space-efficiency of ROBDD[$\wedge_{\widehat{\infty}}$] is comparable with that of d-DNNF and that of another canonical generalization of \ROBDD{} called SDD. read more

PDF Abstract
No code implementations yet. Submit your code now

Tasks


Datasets


  Add Datasets introduced or used in this paper

Results from the Paper


  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

Methods


No methods listed for this paper. Add relevant methods here