Binary Decision Diagrams

A propositional formula is determined up to logical equivalence by its truth table. If the formula has n variables then its truth table requires space Ω(2n) to represent. In this lecture we introduce a data structure called a binary decision diagram which gives a representation that is potentially much more compact. We furthermore show how binary decision diagrams can be used to decide satisfiability, validity, and logical equivalence. While binary decision diagrams have been used successfully in practice, they don’t allow us to circumvent the worst-case difficulty of the various computational problems associated with propositional logic. Indeed, since there are 22 n different formulas on n variables up to logical equivalence, we need space Ω(2n) in the worst case to represent formulas up to logical equivalence.