P ≠ P - Why Some Reasoning Problems Are More Tractable Than Others

Markus Krötzsch

Abstract: Knowledge representation and reasoning leads to a wide range of computational problems, and it is of great interest to understand the difficulty of these problems. Today this question is mainly studied using computational complexity theory and algorithmic complexity analysis. For example, entailment in propositional Horn logic is P-complete and a specific algorithm is known that runs in linear time. Unfortunately, tight algorithmic complexity bounds are rare and often based on impractical algorithms (e.g., O(n 2.373) for transitive closure by matrix multiplication), whereas computational complexity results abound but are very coarse-grained (e.g., many P-complete problems cannot be solved in linear time).