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

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3.2.19 Exotic operators CORAL also provides a few more specific ROBDD algorithms for the purpose of building (efficiently) some ROBDDs representing particular classes of Boolean functions that are often encountered in groundness analysis. Functions of type v =⇒ v1 ∧ v2 ∧ . . . ∧ vn ROBDDs for this class of functions are built by the if_conj algorithm, which takes v and the set of variables V = v1, v2, . . . vn , v /∈ V as its arguments. If all variables in V are greater than v in the ordering the task is trivial, as the result is simply a ROBDD whose root is labeled by v, has 1 as its false successor and has the ROBDD representing v1 ∧ v2 ∧ . . . ∧ vn as its true successor: that’s why we start by considering only the grater variables and building the ROBDD for them. The smaller variables are handled later, as you can see in Algorithm 19. Require: a variable v and a set of variables V function if_conj(v, V ) nv = and_vs_true 1, x ∈ V . v ≺ x nv = make_node v, nv, 1 S = x ∈ V . x ≺ v if S = ∅ then return nv else fv = make_node v, 0, 1 curr = prev = nv while S = ∅ do m = max(S) curr = make_node m, prev, fv prev = curr S = S \ m return curr Functions of type v ⇐⇒ v1 ∧ v2 ∧ . . . ∧ vn Algorithm 19: The if_conj function. ROBDDs for this class of functions are built by the iff_conj algorithm, which takes v and the set of variables V = v1, v2, . . . vn , v /∈ V as its arguments. As for if_conj, the construction is trivial if all variables in V are greater than v in the ordering, as the result is simply a ROBDD whose root is labeled by v, has the ROBDD representing ¬v1∨¬v2∨. . .∨¬nn as its false successor and has the ROBDD representing v1∧v2∧. . .∧vn as its true successor: that’s why, as for if_conj, we start by considering only the greater variables and handle the smaller ones later. Pseudo-code is given in Algorithm 20. 3.2 ROBDD algorithms 30
Require: a variable v and a set of variables V function iff_conj(v, V ) G = x ∈ V . v ≺ x tv = and_vs_true(1, G) fcurr = fprev = 0 while G = ∅ do m = max(G) fcurr = make_node m, fprev, 1 fprev = fcurr G = G \ m nv = make_node v, tv, fcurr S = x ∈ V . x ≺ v if S = ∅ then return nv else fv = make_node v, 0, 1 curr = prev = nv while S = ∅ do m = max(S) curr = make_node m, prev, fv prev = curr S = S \ m return curr Algorithm 20: The iff_conj function. 3.2 ROBDD algorithms 31
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 and 22: We have four terminal cases (note t
Page 23 and 24: Case 4 If fvar = hvar < gvar, retur
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: 3.2.18 Forcing some variables to be
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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