Using Approximation Hardness to Achieve Dependable Computation

Redundancy has been utilized to achieve fault tolerant computation and to achieve reliable communication in networks of processors. These techniques can only be extended to computations solely based on functions in one input in which redundant hardware or software (servers) are used to compute intermediate and end results. However, almost all practical computation systems consist of components which are based on computations with multiple inputs. Wang, Desmedt, and Burmester have used AND/OR graphs to model this scenario. Roughly speaking, an AND/OR graph is a directed graph with two types of vertices, labeled ∧-vertices and ∨-vertices. In this case, processors which need all their inputs in order to operate could be represented by ∧vertices, whereas processors which can choose one of their “redundant” inputs could be represented by ∨-vertices. In this paper, using the results for hardness of approximation and optimization problems, we will design dependable computation systems which could defeat as many malicious faults as possible. Specifically, assuming certain approximation hardness result, we will construct k-connected AND/OR graphs which could defeat a ck-active adversary (therefore a ck-passive adversary also) where c > 1 is any given constant. This result improves a great deal on the results for the equivalent communication problems.