Based on the common properties of logic formulas:equivalence and satisfiability,the concept of variable minimal formulas with property preservation is introduced.A formula is variable minimal if the resulting sub-formulas with any variable omission will change the given property.Some theoretical results of two classes:variable minimal equivalence(VME) and variable minimal satisfiability(VMS) are studied.We prove that VME is NP-complete,and VMS is in DP and coNP-hard.
