Binary Decision Diagram

Explanation

- A **Binary Decision Diagram (BDD)** is a data structure used to represent boolean functions. It uses a directed acyclic graph where each node represents a decision based on a variable, and the edges represent the outcomes of that decision.

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• Steps

  • Construct the decision diagram: Represent the boolean function in terms of binary decisions.
    • The diagram is built such that each node represents a binary decision based on a variable.
    • The edges represent the outcome of that decision (true or false).
  • Minimize the diagram: After constructing the initial BDD, apply techniques (like reduction rules) to minimize the number of nodes and edges. This step makes the BDD more efficient for function evaluation.
  • Evaluate the boolean function: Once the BDD is constructed, evaluate the function by traversing the tree-like structure and applying the decisions.

• Time Complexity

  • O(n) for evaluating the boolean function, but complexity can vary depending on the size and structure of the diagram.
  • Construction: O(n) where n is the number of variables, assuming the boolean function is represented as a decision tree.
  • Evaluation: O(n) for evaluating the function, where n is the number of variables in the BDD (traversing each node once).