On the riddle of coding equality function in the garden hose model

Recently, Harry Buhrman et al introduced a novel communication complexity model, called “garden-hose”. This model sprout from a research on using quantum properties to allow for position based cryptography. SAT is one of the fundamental NP-Complete problem - finding a satisfying assignment to a CNF (conjunctive Normal Form) formula, or proving that none exists. We will not get into the details of the quantum physics, neither we are going to explain the internal work of SAT solver. Instead we will start from the mathematical garden hose model; describe the way we used SAT solver as a tool; give some lower and upper bounds on implementing the equality function; and conclude with open questions.