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

More documents

Recommendations

Info

Require: a ROBDD node n and a set of variables F function and_vs_false(n, F ) avf_impl(n, F, 1) function avf_impl(n, F, c) if n = 0 then return n else if n = 1 then nres = 1 while xc max(F ) do nres = make_node max(F ), 0, nres F = F \ max(F ) return nres else if nvar ≺ xc then return make_node nvar, avf_impl(ntrue, F, c), avf_impl(nfalse, F, c) else if xc nvar then nnext = n else nnext = nfalse if ∃xnext = min {x ∈ F . xc ≺ x} then return make_node(xc, 0, avf_impl(nnext, F, variable_index(xnext))) else return make_node(xc, 0, nnext) Algorithm 18: The and_vs_false function 3.2 ROBDD algorithms 28
3.2.18 Forcing some variables to be equivalent in a positive function The algorithm expand_equivalent_vars can be used to perform efficiently the inverse operation for the one presented in 3.2.15, that is conjuncting a Boolean function with the equivalence conditions given by an equivalence relation, for the case when f ∈ Pos. Given a ROBDD representing f and the equivalence relation L, we define the current variable xc and the set of true leaders T ; the first is initialized to the smallest variable in dom(L), while the second is initialized to ∅. Afterwards, we start from the root of the ROBDD and follow these steps: Step 1 If this node is 1 return the result of the application of the algorithm make_equivalent_vars (presented in 3.2.10) on the same relation L, using the same values for xc and T . Step 2 If this node if 0 return 0. Step 3 If xc is undefined (which means that we have already processed all variables in dom(L)) return the current node. Step 4 Let x be the variable by which this node is labeled. If x ≺ xc return the node labeled with x and having the results of the recursive calls of this algorithm (with the same values for xc and T ) on the true and false successors of the current node as its true and false successors respectively. Step 5 Let xn be the smallest variable in dom(L) that is greater than xc. If x = xc then xc must be a leader for L, so we return the node labeled with xc, having the result of the recursive application of this algorithm on the true successor of this node with xn as the current variable and with T = T ∪ {xc} as its true successor and the result of the recursive application of this algorithm on the false successor of this node with xn as the current variable and with the same old value of T as its false successor. Step 6 Otherwise, let xl = λL(xc). If xl = xc then xc is a leader for L so we return the node labeled with xc, having the result of the recursive application of this algorithm on this same node with xn as the current variable and with T = T ∪ {xc} as its true successor and the result of the recursive application of this algorithm on this same node with xn as the current variable and with the same old value of T as its false successor. Step 7 If xl ∈ T return the node labeled with xc, having the result of the recursive application of this algorithm on this same node with xn as the current variable and with the same value of T as its true successor and 0 as its false successor. Step 8 Otherwise, return the node labeled with xc, having the result of the recursive application of this algorithm on this same node with xn as the current variable and with the same value of T as its false successor and 0 as its true successor. 3.2 ROBDD algorithms 29
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: Step 1 If the node is 0 return this
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.

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

Create successful ePaper yourself

Delete template?

Save as template?