ROBDD as a recursively defined periodic bit-string

Abstract

The paper describes bit-string interpretation of ROBDDs. ROBDDs are viewed as recursively defined periodic bitstrings and BDD operations as recursively defined bitwise operations. Using the periodicity of bit-strings, we prove that the ROBDDs generated by rotating the bitstring of a ROBDD are mutually different. It implies not only the exponential BDD size but also more compact BDD representation. And the interpretation can explain the hidden ideas of variable ordering. [Def. 51 A negative n-fold concatenation of bit-string: PBS(Of3= h (null string), PBS(n,fl = BS(flPBS(n+l,fl ifn < 0. Similarly, BPBS(b,j) = PBS(-2-b,fl i f b < 0 . BS"cfl E PBS(-"f3PBS( w,f3 Fb(x,Bs(')= x-th symbol of BS# i f 0 5 x < 24 and Fb(x-24 BS(f3) = Fb(x+2',Bscfl) = Fb(x,BScfl)for integer x and non-negative integer b.[Def. 61 An infinite log-periodic Boolean function :By above definitions, BS(F,(x,BS(v))) = BS"(v) for a ROBDD node v. Note that Fb(x+r,BS(V)) = Fb(x,Bs(w))