Abstract
This paper shows that the class of monotone functions coincides with the class of deadlock disjunctive normal forms. The paper introduces the concept of singletier deadlock disjunctive normal forms. A formula is obtained by calculating the number of these functions on all tiers of an n-dimensional cube. This paper proposes an algorithm for finding monotone functions that are single-tier deadlock disjunctive normal forms for n variables. Calculations are performed to calculate single-tier deadlock disjunctive normal forms for n=1,2,…13. Monotone functions of n variables can be defined on the vertices of an n-dimensional cube. A theorem is given that decomposes the monotone functions of n variables into two classes: the monotone functions of n-1 variable and the monotone functions of n variables that label only the variable x1. A second method for computing single-tier deadlock disjunctive normal forms is proposed using this theorem.