Backward consistency and sense of direction in advanced distributed systems

Studies on the relationship between label consistency, computability, and complexity assume the existence of local orientation; this assumption is in fact at the basis of the point-to-point model and is realistic for systems where a communication link can connect only two entities. However, in systems which use more advanced communication and interconnection technology, such as buses, optical networks, and wireless communication media, and more importantly, in heterogeneous systems (such as the Internet) which include any combination of the above, local orientation cannot be assumed. This implies that the entire established body of results on the relationship between label consistency (e.g., sense of direction) and computability and complexity does not hold for systems with advanced communication technology. In this paper we consider a new type of consistency which we shall call backward consistency and which, unlike sense of direction, can exist even without local orientation. Thus, unlike all previous forms of consistency, it can be found (or designed) in advanced distributed systems. We study backward consistency both in terms of its relationship with the traditional properties of local orientation and (weak) sense of direction, and with respect to symmetries of the edge labelings and of the naming functions. We show that backward consistency is computationally equivalent to sense of direction; in other words, it is possible to take advantage of the computational power of sense of direction even in the absence of local orientation.