Learning Ordered Binary Decision Diagrams

  title={Learning Ordered Binary Decision Diagrams},
  author={Ricard Gavald{\`a} and David Guijarro},
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… 

An Efficient Exact Learning Algorithm for Ordered Binary Decision Diagrams

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

On the Hardness of Approximating the Minimum Consistent OBDD Problem

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

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

Learnability of Some Eecient Representations of Boolean Functions

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

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

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

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

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.



Improving the Variable Ordering of OBDDs Is NP-Complete

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

The Complexity of the Optimal Variable Ordering Problems of Shared Binary Decision Diagrams

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.

Symbolic Boolean manipulation with ordered binary-decision diagrams

The OBDD data structure is described and a number of applications that have been solved by OBDd-based symbolic analysis are surveyed.

Learning μ-branching programs with queries

We show that the class of p-branching programs can be exactly learned in ()(rz5) time us:n$ only O(n) equivalence queries and O(n ) membership queries, but neither type of query alone is sufficient

Computers and Intractability: A Guide to the Theory of NP-Completeness

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.

Negative results for equivalence queries

  • D. Angluin
  • Computer Science, Mathematics
    Mach. Learn.
  • 1990
There is no polynomial time algorithm using only equivalence queries that exactly identifies deterministic or nondeterministic finite state acceptors, context free grammars, or disjunctive or conjunctive normal form boolean formulas.

The Complexity of Equivalence and Containment for Free Single Variable Program Schemes

Non-containment for free single variable program schemes is shown to be NP-complete. A polynomial time algorithm for deciding equivalence of two free schemes, provided one of them has the predicates

Design and analysis of efficient learning algorithms

  • R. Schapire
  • Computer Science
    ACM Doctoral dissertation award ; 1991
  • 1992