Unique Satisfiability of Horn Sets Can Be Solved in Nearly Linear Time

Abstract If a Horn set I has a single satisfying truth assignment or model then that model is said to be unique for I . The question of determining whether a unique model exists for a given Horn set I is shown to be solved in O (α(L)∗L) time, where L is the sum of the lengths of the clauses in I and α is the inverse Ackermann function. It is also shown that if L⩾A∗ log (A) where A is the number of distinct proposition letters then unique satisfiability can be determined in O( L ) time.