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

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Require: an ROBDD node n and a set of variables E function elim_search_true_vars(n, E) if is_leaf(n) then return (n, E) else if nvar ∈ E or nfalse = 0 then E = E ∪ nvar return (elim_search_true_vars(ntrue, E), E) else if E = ∅ or max(E) ≺ nvar then return (n, E) else return (make_node nvar, elim_true_vars(ntrue, E), elim_true_vars(nfalse, E) , E) Algorithm 15: The elim_search_true_vars function. Require: an ROBDD node n and a set of variables D function elim_search_false_vars(n, D) if is_leaf(n) then return (n, D) else if nvar ∈ D or ntrue = 0 then D = D ∪ nvar return (elim_search_false_vars(nfalse, D), D) else if D = ∅ or max(D) ≺ nvar then return (n, D) else return (make_node nvar, elim_false_vars(ntrue, D), elim_false_vars(nfalse, D) , D) Algorithm 16: The elim_search_false_vars function. 3.2 ROBDD algorithms 26
Step 1 If the node is 0 return this node. Step 2 If the node is 1 build and return the ROBDD for Boolean function xc ∧ xc+1 ∧ . . . ∧ xn (how to build it is trivial and is shown in Algorithm 17). Step 3 If the variable x by which this node is labeled is smaller than xc return the ROBDD whose root is labeled by x and whose true and false successors are the results of the application of this algorithm on the true and false successors of this node respectively. Step 4 Let t be this node if xc x or its true successor otherwise. If xc is the greatest variable in G, then return the ROBDD having its root labeled with c, t as its true successor and 0 as its false successor; otherwise return the ROBDD having its root labeled with c, the result of the recursive application of this algorithm on t as its true successor and 0 as its false successor. You can find the pseudo-code for both algorithms in Algorithm 17 and Algorithm 18. Require: a ROBDD node n and a set of variables T function and_vs_true(n, T ) avt_impl(n, T, 1) function avt_impl(n, T, c) if n = 0 then return 0 else if n = 1 then nres = 1 while xc max(T ) do nres = make_node max(T ), nres, 0 T = T \ max(T ) return nres else if nvar ≺ xc then return make_node nvar, avt_impl(ntrue, T, c), avt_impl(nfalse, T, c) else if xc nvar then nnext = n else nnext = ntrue if ∃xnext = min {x ∈ T . xc ≺ x} then return make_node(xc, avt_impl(nnext, T, variable_index(xnext)), 0) else return make_node(xc, nnext, 0) Algorithm 17: The and_vs_true function 3.2 ROBDD algorithms 27
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: The implementation is quite simple:
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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