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This paper augments OBDD with conjunctive decomposition to propose ageneralization 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 familyof canonical languages called ROBDD[$\wedge_{\widehat{i}}$], whereROBDD[$\wedge_{\widehat{0}}$] is equivalent to ROBDD. We show that thesuccinctness of ROBDD[$\wedge_{\widehat{i}}$] is strictly increasing when $i$increases. We introduce a new time-efficiency criterion called rapidity whichreflects that exponential operations may be preferable if the language can beexponentially more succinct, and show that: the rapidity of each operation onROBDD[$\wedge_{\widehat{i}}$] 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 ofROBDD[$\wedge_{\widehat{i}}$] is normally not larger than that of theequivalent \ROBDDC{\widehat{i+1}}; b) conjoining twoROBDD[$\wedge_{\widehat{1}}$]s is more efficient than conjoining twoROBDD[$\wedge_{\widehat{0}}$]s in most cases, where the former is NP-hard butthe latter is in P; and c) the space-efficiency ofROBDD[$\wedge_{\widehat{\infty}}$] is comparable with that of d-DNNF and thatof another canonical generalization of \ROBDD{} called SDD.

Augmenting Ordered Binary Decision Diagrams with Conjunctive Decomposition