a modern C++ library for the manipulation of Boolean functions

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Require: three ROBDD nodes i, t and e function ite(i, t, e) if i = 1 then return t else if i = 0 then return e else if t = 1 and e = 0 then return i else if t = e then return t else xtop = min {ivar, tvar, evar} if xtop = ivar then inewt = itrue inewf = ifalse else inewt = inewf = i if xtop = tvar then tnewt = ttrue tnewf = tfalse else tnewt = tnewf = t if xtop = evar then enewt = etrue enewf = efalse else enewt = enewf = e return make_node xtop, ite(inewt, tnewt, enewt), ite(inewf , tnewf , enewf ) Algorithm 3: The ite function 3.2 ROBDD algorithms 16
Case 4 If fvar = hvar < gvar, return make_node fvar, g, hfalse . Case 5 If gvar < fvar < hvar, return make_node gvar, gen_var_ite_h(f, gtrue, h), gen_var_ite_h(f, gfalse, h) . Case 6 If gvar < fvar = hvar or gvar < hvar < fvar, return make_node gvar, gen_var_ite(f, gtrue, h), gen_var_ite(f, gfalse, h) . Case 7 If gvar = hvar < fvar, return make_node gvar, gen_var_ite(f, gtrue, htrue), gen_var_ite(f, gfalse, hfalse) . Case 8 If hvar < fvar < gvar, return make_node hvar, gen_var_ite_g(f, g, htrue), gen_var_ite_g(f, g, hfalse) . Case 9 If hvar < fvar = gvar or hvar < gvar < fvar, return make_node hvar, gen_var_ite(f, g, htrue), gen_var_ite(f, g, hfalse) . The set of cases for var_ite is a strict subset of these cases, obtained by removing the ones where fvar = gvar or fvar = hvar and replacing all calls to gen_var_ite, gen_var_ite_h and gen_var_ite_g with calls to var_ite, var_ite_h and var_ite_g respectively. 3.2.7 Variables on which a Boolean function depends The algorithm vars which takes a ROBDD representing the Boolean function f and returns vars(f) can be easily implemented by visiting the ROBDD and collecting the variables that label the nodes. This algorithm is one of the few ROBDD algorithms in CORAL for which no caching is provided. Pseudo-code is given in Algorithm 4. Require: a ROBDD node n function vars(n) if n = 0 or n = 1 then return ∅ else return nvar ∪vars(ntrue) ∪ vars(nfalse) Algorithm 4: The vars function 3.2.8 Entailed and disentailed variables The algorithms entailed_vars and disentailed_vars (and their counterparts entailed_vars_no_cache and disentailed_vars_no_cache, which don’t use caching) are used to compute true(f) and false(f). In order to compute the set of all entailed variables in a ROBDD, we start from its root node and follow these steps (the algorithm that looks for disentailed variables is very similar): 3.2 ROBDD algorithms 17
Page 1 and 2: UNIVERSITÀ DEGLI STUDI DI PARMA Fa
Page 3 and 4: Abstract The purpose of this work i
Page 5 and 6: 3.2.9 Combined search for entailed,
Page 7 and 8: 1 Boolean functions 1.1 Fundamental
Page 9 and 10: L is denoted as leaders(L) and its
Page 11 and 12: 2 Reduced Ordered Binary Decision D
Page 13 and 14: onto nfalse if a(nvar) = 0, otherwi
Page 15 and 16: operator has a dominant value (for
Page 17 and 18: 3 Algorithms in CORAL 3.1 Basic dat
Page 19 and 20: 1 inline const ROBDD* 2 ROBDD::and_
Page 21: We have four terminal cases (note t
Page 25 and 26: 3.2.9 Combined search for entailed,
Page 27 and 28: Step 1 If the node is 1 or 0 return
Page 29 and 30: Step 5 If λR(xi) ∈ T return the
Page 31 and 32: The implementation is quite simple:
Page 33 and 34: Step 1 If the node is 0 return this
Page 35 and 36: 3.2.18 Forcing some variables to be
Page 37 and 38: Require: a variable v and a set of
Page 39 and 40: Require: a set of variables V funct
Page 41 and 42: 4.1.2 Implementation policies The N
Page 43 and 44: 4.2 Algorithms with composite repre
Page 45 and 46: Require: n, E, D, L function norm
Page 47 and 48: more. Formally, given m composite r
Page 49 and 50: 5 Experimental evaluation 5.1 Metho
Page 51 and 52: 5.2 Results 5.2.1 Plain ROBDD repre
Page 53 and 54: Program China China + CORAL Differs
Page 57 and 58: 5.2.3 ROBDD plus entailed and equiv
Page 61: Bibliography [Bry86] R. E. Bryant.

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