Questions related to binary decision diagrams.
Questions tagged [bdd]
19 questions
3
votes
1 answer
What is the main difference between binary decision tree and binary decision diagram(BDD)?
What is the main difference between binary decision tree and binary decision diagram(BDD)? From what I can tell I only understand that a binary decision diagram is a more compact representation because it eliminates nodes that have both edges…
Teodorico Levoff
- 431
- 1
- 4
- 13
3
votes
1 answer
The complexity of BDD Synchronous Composition
As shown in Byrant's original paper, the time complexity of (single-variable) composition algorithm is cubic, and it is a tight upper bound. My question is about synchronous composition, written as
$$f' = f(x_{1},\dots,x_{n})|_{x_1=g_1, \dots,…
doganulus
- 356
- 2
- 7
3
votes
0 answers
Knowing if I have an optimal ordering for a OBDD
I'm learning about OBDD and I have learned that the size of a reduced OBDD (ROBDD) is dependent on the ordering of the variables, and that finding an optimal ordering is an NP hard problem.
Say I already have one ROBDD by some ordering, I can, in…
Belgi
- 267
- 1
- 9
3
votes
1 answer
Counting words that satisfy SAT-like constraints with BDDs
I have the following #P-complete problem:
Given an alphabet $\Sigma$ and a matrix $M$ where each entry can be a symbol from $\Sigma$ or the wildcard symbol $*$, find the number of strings $s$ with the property that there exists $i$ such that for all…
Elliot Gorokhovsky
- 923
- 4
- 15
2
votes
1 answer
Multiplication function BDD size lower bounds
Randal Bryant developed an exponential size lower bound for any BDD encoding the middle bit output of the multiplication function, regardless of variable permutation.
But at the same time the multiplication function is decidable in logarithmic…
user23893
2
votes
1 answer
What are the differences between parse and decision trees?
I have created a parse tree for the formula: a∧¬(b∨c)∨¬d∧(¬b) successfully.
I am now asked to create a decision tree for the same formula. What are the main differences between a parse tree and a decision tree?
Djoni
- 33
- 3
2
votes
1 answer
Algorithm for completeness of bit patterns with wildcards
Consider a list of bit patterns, each N bits long, and consisting of 0s, 1s, and x's to denote wildcards. For example, for N=8:
0110xx11
1111xx00
111xxxx1
10000000
...
Is there an algorithm for determining whether the list of bit patterns fully…
Mike
- 23
- 2
2
votes
0 answers
Difference between fully-reduced BDD and quasi-reduced BDD
I am trying to figure out difference between fully- and quasi-reduced BDDs. I have read a lot of material but still it is not very clear. As I am trying to figure out the quasi reduced version for union between two BDDs.
The algorithm for union…
compengr
- 21
- 1
2
votes
0 answers
Efficient integer multiplication using BDDs and fixed point
Suppose we have two sets A,B of size n,k respectively, being sets of nonnegative integers each encoded with N bits, and we'd like to form a set of bitstrings of length 3N and [maximum] size n*k such that they represent all possible multiplication of…
Troy McClure
- 644
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- 10
1
vote
0 answers
How to Construct Kripke Structure States from Nested Functions
Say I have these defined functions:
function a(x, y, z){
var q = b(y)
q = c(q, z, x)
q = d(q)
return q
}
function b(x) {
var q = e(x)
q = f(q)
return q
}
function c(x, y, z) {
return x + y * z
}
function d(x) {
return x *…
Lance Pollard
- 2,323
- 1
- 19
- 34
1
vote
0 answers
Understanding a Single Step in the Model Checking Algorithm
This answer explains roughly how to convert a nested boolean function into a Binary Decision Diagram (BDD). This question is about how to structure the states for the BDD. Now in this question I am trying to understand how to process the program…
Lance Pollard
- 2,323
- 1
- 19
- 34
1
vote
0 answers
Pairwise (partial) equivalence of boolean functions
I have a bunch of boolean functions, say $b_1,b_2,\dots,b_k \colon \{0,1\}^m \to \{0,1\}^n$, all given in terms of circuits.
I want to determine for which inputs they pairwise agree, that is, I want to compute, for all $b_i, b_j$ with $i \neq j$ the…
Mens
- 11
- 1
0
votes
2 answers
BDD to CNF in linear time
I have a book from my university that claims:
There is an linear algorithm that can convert BDD to CNF in linear time, and generate CNF in linear length of the BDD size (number of nodes).
Then they wrote an exercise to find one...
Actually I…
nrofis
- 198
- 11
0
votes
1 answer
Creating a decision tree?
So I'm trying to split on an attribute "Color" that has possible values (Blue,Green,Red,Orange,Pink).
I'm splitting on entropy values, and the best split can either be Multi-Way 5, Multi-Way 4, Multi-Way 3, or Binary. For example:
5: (Blue,…
ocean800
- 125
- 4
0
votes
1 answer
Is the number of nodes in an ORBDD 2n + 2?
Wikipedia says that the number of nodes in a ORBDD (Order Reduced Binary Decision Diagrams) of order $x_1 < x_2 < \dots < x_{2n}$ is $2n + 2$.
But I can't find proof. Anyone?
kaitlynrutledge
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- 5