Results 1 
4 of
4
The Complexity of Automated Reasoning
, 1989
"... This thesis explores the relative complexity of proofs produced by the automatic theorem proving procedures of analytic tableaux, linear resolution, the connection method, tree resolution and the DavisPutnam procedure. It is shown that tree resolution simulates the improved tableau procedure and th ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
This thesis explores the relative complexity of proofs produced by the automatic theorem proving procedures of analytic tableaux, linear resolution, the connection method, tree resolution and the DavisPutnam procedure. It is shown that tree resolution simulates the improved tableau procedure and that SLresolution and the connection method are equivalent to restrictions of the improved tableau method. The theorem by Tseitin that the DavisPutnam Procedure cannot be simulated by tree resolution is given an explicit and simplified proof. The hard examples for tree resolution are contradictions constructed from simple Tseitin graphs.
Towards Tableau TheoremProving with Analytic Cut
"... this paper, we discuss some initial results in implementing theoremprovers with analytic cut. We also outline our overall research programme, which is to develop a general framework for firstorder theoremproving in classical and nonclassical logics. This framework is to be based on (some suitabl ..."
Abstract
 Add to MetaCart
this paper, we discuss some initial results in implementing theoremprovers with analytic cut. We also outline our overall research programme, which is to develop a general framework for firstorder theoremproving in classical and nonclassical logics. This framework is to be based on (some suitable implementation of) the system KE [Mondadori, 1988], in which analytic cut plays a central role. 2 Preliminary Investigations
NorthHolland Publishing Company A NOTE ON SOME COMPUTATIONALLY DIFFICULT SET COVERING PROBLEMS
, 1978
"... Fulkerson et al. have given two examples of set covering problems that are empirically difficult to solve. They arise from Steiner triple systems and the larger problem, which has a constraint matrix of size 330 × 45 has only recently been solved. In this note, we show that the Steiner triple system ..."
Abstract
 Add to MetaCart
Fulkerson et al. have given two examples of set covering problems that are empirically difficult to solve. They arise from Steiner triple systems and the larger problem, which has a constraint matrix of size 330 × 45 has only recently been solved. In this note, we show that the Steiner triple systems do indeed give rise to a series of problems that are probably hard to solve by implicit enumeration. The main result is that for an n variable problem, branch and bound algorithms using a linear programming relaxation, and/or elimination by dominance require the examination of a superpolynomial number of partial solutions