A Space Hierarchy for k-DNF Resolution

The k-DNF resolution proof systems are a family of systems indexed by the integer k, where the k member is restricted to operating with formulas in disjunctive normal form with all terms of bounded arity k (k-DNF formulas). This family was introduced in [Krajı́ček 2001] as an extension of the wellstudied resolution proof system. A number of lower bounds have been proven on k-DNF resolution proof length and space, and it has also been shown that (k+1)-DNF resolution is exponentially more powerful than k-DNF resolution for all k with respect to length. For proof space, however, no corresponding hierarchy has been known except for the (very weak) subsystems restricted to tree-like proofs. In this work, we establish a strict space hierarchy for the general, unrestricted k-DNF resolution proof systems.