Research on the muddy children puzzle problem

Abstract

Muddy children puzzle is a well-spread mathematical puzzle. It can be solved by two ways, which are Kripke Structure and true and false statement. The model checking problem is solved by searching the state space of the system. Ideally, the verification is completely automatic. The main challenge is the state explosion problem. The problem occurs in systems with many components that can interact with each other, so that the number of global states can be enormous. This paper observes that any propositional planning problem can be modeled as an LTL model checking problem as any propositional goal g can be expressed in the form of a counterexample to the temporal formula in LTL. If the problem is solvable, the LTL model checker will return a counterexample, which manifests a solution for the planning problem. This paper shows that the puzzle is solvable for any number of agents if and only if the quantifier in the announcement is positively active (satisfies a form of variety).