# Learning Ordered Binary Decision Diagrams

@inproceedings{Gavald1995LearningOB, title={Learning Ordered Binary Decision Diagrams}, author={Ricard Gavald{\`a} and David Guijarro}, booktitle={ALT}, year={1995} }

This note studies the learnability of ordered binary decision diagrams (obdds). We give a polynomial-time algorithm using membership and equivalence queries that finds the minimum obdd for the target respecting a given ordering. We also prove that both types of queries and the restriction to a given ordering are necessary if we want minimality in the output, unless P=NP. If learning has to occur with respect to the optimal variable ordering, polynomial-time learnability implies the…

## 24 Citations

### An Efficient Exact Learning Algorithm for Ordered Binary Decision Diagrams

- Computer ScienceALT
- 1997

A new algorithm which exactly learns ordered binary decision diagrams (OBDDs) with a given variable ordering via equivalence queries and membership queries is proposed.

### An efficient query learning algorithm for ordered binary decision diagrams

- Computer ScienceInf. Comput.
- 2005

### On the Hardness of Approximating the Minimum Consistent OBDD Problem

- Computer ScienceSWAT
- 1996

It is proved that there is a constant e > 0 such that no polynomial time algorithm can approximate the minimum consistent OBDD within the ratio ne unless P=NP, where n is the number of variables.

### Query Learning of Bounded-Width OBDDs

- Computer ScienceALT
- 1996

This paper presents a learning algorithm for width-2 OBDDs, an algorithm which uses O(n3) equivalence queries alone, and shows a negative result: that there are no polynomial-time algorithms capable of learning width-3 O BDDs from proper equivalence query alone.

### On the influence of the variable ordering for algorithmic learning using OBDDs

- Computer ScienceInf. Comput.
- 2005

### Learnability of Some Eecient Representations of Boolean Functions

- Computer Science, Mathematics
- 2007

This thesis studies the learnability of several representation classes of Boolean functions: a restriction on k-term DNF, ordered binary decision diagrams and monotone term decision lists. We also…

### On the Hardness of Approximating the minimum Consistent Acyclic DFA and Decision Diagram

- MathematicsInf. Process. Lett.
- 1998

### Testing Computability by Width-2 OBDDs Where the Variable Order is Unknown

- Computer Science, MathematicsCIAC
- 2010

This work designs and analyzes an algorithm for testing functions for the property of being computable by a read-once width-2 Ordered Binary Decision Diagram, also known as a branching program, where the order of the variables is not known to us.

### Exponential Lower Bounds on the Space Complexity of OBDD-Based Graph Algorithms

- Computer Science, MathematicsLATIN
- 2006

This work extends by concrete exponential lower bounds on the space complexity of OBDD-based algorithms for the Reachability Problem, the Single-Source Shortest-Paths Problem, and the Maximum Flow Problem by establishing the first exponential lower bound on the O BDD size for the highest bit of Integer Multiplication w.

### Lower Bounds for Testing Computability by Small Width OBDDs

- Computer Science, MathematicsTAMC
- 2011

This work considers the problem of testing whether a function f is computable by a read-once, width-2 ordered binary decision diagram (OBDD), and shows that for any constant w ≥ 4, Ω(n) queries are required, resolving a conjecture of Goldreich.

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Ordered binary decision diagrams are a useful representation of Boolean functions, if a good variable ordering is known. Variable orderings are computed by heuristic algorithms and then improved with…

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It is proved that the optimal variable ordering problem of shared BDD's is NP-complete, and touch on the hardness of this problem and related problems of B DD's.

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The experiences, understandings, and beliefs that guide the professional practices of teacher educators are explored, and the book paints a picture of a profession that offers huge rewards, alongside challenges and frustrations.

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