# OBDD

AcronymDefinition
OBDDOrdered Binary Decision Diagram
OBDDOrdered Bicontinuous Double Diamond
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Experimental Results for the Verification of State Reachability Tool SMV Technique OBDD Examples Scale mem (MB) time (sec) Dining philosophers Philosophers 6 1.0 0.6 (Operating System) 8 1.1 4.6 10 2.6 57.6 12 11.3 1,277.9 14 62.4 40,764.8 Client & Server clients/servers (Round-Robin) 3/1 1.0 2.6 4/1 4.7 1,531.3 5/1 129.8 685,405.4 In this article, we present a new technique for detecting a reachable marking (or submarking) as shown in Section 10.
by a Boolean function and represented by an OBDD) where f is true by a fixpoint computation.
When the conjunction (AND) operation is executed on f(V') and TR(V, V'), the resulting OBDD TR'(V, V') characterizes the transitions from states in g(V) to states in f(V').
The resulting OBDD represents the set of next-state r(V') reachable from states in Init(V) in one step.
As a result, we can represent the transition relation between x and x' by an OBDD over c, x, and x'.
In this section, we review the concept of ordered binary decision diagrams (OBDD) and Multivalued Decision Diagram (MDD).
An ordered binary decision diagram (OBDD) is a BDD with a constant order for Boolean variables.
For example, Figure 1 shows the complete binary tree (Figure 1(a)) and the OBDD (Figure 1(b)) for the Boolean expression W = [x.sub.1] * [x.sub.2] + [x'.sub.1] * [x.sub.3] with the variable order n : [x.sub.3] > [x.sub.2] > [x.sub.1].
Basically, our approach may provide a useful supplement to existing methods based on OBDD or SAT and may also provide important theoretical insights by allowing the application of important results in symbolic computation to the assertion checking problems.
We have incorporated the OBDD construction algorithm for linear constraints into SMV and tested our implementation on two examples.
In particular, we give an efficient algorithm for constructing OBDDs (Ordered Binary Decision Diagrams) for linear constraints among integer variables.
A FAST ALGORITHM FOR BUILDING OBDDS FOR LINEAR CONSTRAINTS
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