An n log n Algorithm for Online BDD Refinement

Nils Klarlund
1995 BRICS Report Series  
Binary Decision Diagrams are in widespread use in verification systems<br />for the canonical representation of Boolean functions. A BDD representing<br />a function phi : B^nu -> N can easily be reduced to its canonical form in<br />linear time.<br />In this paper, we consider a natural online BDD refinement problem<br />and show that it can be solved in O(n log n) if n bounds the size of the<br />BDD and the total size of update operations.<br />We argue that BDDs in an algebraic framework
more » ... uld be understood<br />as minimal fixed points superimposed on maximal fixed points. We propose<br />a technique of controlled growth of equivalence classes to make the<br />minimal fixed point calculations be carried out efficiently. Our algorithm<br />is based on a new understanding of the interplay between the splitting<br />and growing of classes of nodes.<br />We apply our algorithm to show that automata with exponentially<br />large, but implicitly represented alphabets, can be minimized in time<br />O(n log n), where n is the total number of BDD nodes representing the<br />automaton.
doi:10.7146/brics.v2i29.19931 fatcat:vuy4lqvhjjak5avelvpms4jaau