Models For Dependable Computation with Multiple Inputs and Some Hardness Results

We consider the problem of dependable computation with multiple inputs. The goal is to study when redundancy can help to achieve survivability and when it cannot. We use AND/OR graphs to model fault tolerant computations with multiple inputs. While there is a polynomial time algorithm for finding vertex disjoint paths in networks, we will show that the equivalent problem in computation systems with multiple inputs is NP-hard. Our main results are as follows. (1) We present a general model for fault tolerant computation systems with multiple inputs: AND/OR graphs. (2) We show that it is NP-hard to find two vertex disjoint solution graphs in an AND/OR graph. It follows that in the general case redundancy cannot help to achieve survivability, assuming P 6=NP. ∗Research supported by DARPA F30602-97-1-0205. Part of this work was done while the authors were at the University of Wisconsin–Milwaukee. 2 Wang, Desmedt, Burmester/Introduction