An improved version of width restricted resolution

A new form of width restricted resolution, called \CUBI resolution" (\closure under bounded input resolution") is presented. CUBI resolution allows to eliminate the dependence on the maximal input clause length in the general lower bound for resolution from Ben-Sasson, Wigderson 99], and also the poly-time decidability problem about \k-resolution" ((Kleine B uning 93]) is bypassed (by slightly strengthening the calculus). Generalizing the well-known equivalence of the refutation power of Unit resolution and input resolution, CUBI resolution simulates \nested input resolution." 1 Introduction 1.1 Two forms of width restricted resolution Lower bounds for resolution complexity via width lower bounds 1975 Galil introduced bounded resolution in 9], using only clauses of bounded size, and he showed that certain Tseitin-type formulas in 3-CNF require very long clauses in any (full) resolution refutation, expressing hope, that this result might be useful for a super-polynomial lower bound for (full) resolution.