Extended Impossibility Results for Asynchronous Complete Networks

It is proved that a large class of distributed tasks cannot be solved in the pr,2s,2nct~ of faulty procc:isor~ Thb, class cmnaills tasks whose unsolvahility ill 111,2 pr,2senc,2 of faalls is knowB (tile cons,211sus task a~ld il!, wltianls, of. Fischer ,21 at. (1985)) as w,dl as some new tasks (e.g., constructing a sF, alming Ire,2). In parlicular, we hitroduce the notion of the decasion graph of a task. and show that cvcry problem whose 4.lcgisioil graph is disconnected cannot be solved in the presence of one faulty processor, By reducing the unsotval)ility of this problem to the un~olvability of tile cons,2nsus problem. The notion of unsolvability us,2d here is very wolff.: We say that a proto`2o! solves a given problem in spite of one hmity pro,.,2ssor if in any execution it sztisfies (i) all nonfauhy processors eventually halt, and (it) if no processor is faulty, it solves the problem, Hence. the unsolvahility of a problem in this model implies its unsolvability in other models appearing in the literature.