We describe BDD-based decision procedures for K . Our approach is inspired by the automata-theoretic approach, but we avoid explicit automata construction. Our algorithms compute the fixpoint of a set of types, which are sets of formulas satisfying some consistency conditions. We use BDDs to represent and manipulate such sets. By viewing the sets of types as symbolic encoding of all possible models of a formula, we developed particle-based and lean-vector-based representation techniques which gives more compact representations. By taking advantage of the finite-tree-model property of K , we introduced a level-based evaluation scheme to speed up construction and reduce memory consumption. We also studied the effect of formula simplification on the decision procedures. As part of the benching procedure, we compared the BDD-based approach with a representative selection of current approaches, as well as developing an algorithm to translate K to QBF based on our decision procedure. Experimental results show that the BDD-based approach dominates for modally heavy formulas, while search-based approaches dominate for propositionally-heavy formulas.