Knot: A knot K in a graph is a nonempty set of nodes such that for every node x in K, all nodes in K and only them are reachable from x.

Phantom deadlock: Because of the lack of global memory, communication occurs solely by messages and sites may obtain out of date and inconcistent WFGs of the system. So, sites may detect a cycle that does not exist but whose different segments were existing in the system at different times.

Probe: These are special fixed-size and normally short messages used by the algorithm. A probe is a triplet (i, j, k) denoting that it belongs to a deadlock detection initiated for process Pi, and it is being sent by the home site of process Pj to the home site of process Pk.

Dependency between processes: A process Pj is said to be dependent on another process Pk if there exists a sequence of processes Pj, Pj1, Pj2, ..., Pjm, Pk such that each process except Pk in the sequence is blocked and each process in the sequence except Pj holds a resource for which the previous process in the sequence is waiting.

Local dependency between processes: Two processes are locally dependent, if they are dependent and also they are at the same site.

Dependent_i (): the system maintains a boolean array dependent_i for all processes Pi, where dependent_i (j) is true only if Pi knows that Pj is dependent on it. Initially, dependent_i (j) is false for all nodes.