# Questions tagged [bdd]

Questions related to binary decision diagrams.

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### What's the relation between DPLL and BDDs?

BDDs are a way of representing Boolean formulas. DPLL is an algorithm to determine satisfiability of Boolean formulas. My understanding is that the two are used for SAT solving. How are they combined?
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### State of the art construction of OBDDs

I have some Boolean functions represented by pretty big Boolean formulas and I need to build OBDDs from the formulas for further manipulation. How to do it is well known with textbook algorithms but I ...
161 views

### 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 ...
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### Compact Shared Reduced Binary Decision Diagrams with negated identifiers

Consider a BDD implementation in which each bdd in the system has a unique positive integer identifying it (thanks to canonicity and as common implementation designs follow, by utilizing a hashmap). I ...
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### 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 ...
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1 vote
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### How to Construct Kripke Structure States from Nested Functions

Say I have these defined functions: ...
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1 vote
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### 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 ...
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### 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 ...
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### 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 ...
121 views

### 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, ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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?