• Races (race conditions) are the situations, where two or more processes are reading or writing some shared data and the final result depends on who runs precisely when.
• Race conditions can be avoided if no two processes are in their critical sectionsat the same time
• We say then that two processes are mutually excluding each other  (to be simultaneously in their critical sections)
• A critical section is the part of the program where processes access their shared variables

By a mutual exclusion problem  we mean a pair: P=(PR,S), where PR={PR1,...,PRn} is the set of processes, and S={S1,...,Sk} is the set of  minimal mutually excluding subsets of PR such that each Sj is the subset of PR and no Sj is the subset of Sm for j different than m

• Any subset of processes from PR may be in their critical sections at the same time iff it does not contain any of the mutually excluding sets from S
• In particular:
• if only one of n processes may enter its critical section at a time, the minimal mutually excluding sets are all pairs of processes,
• if any k<n processes may enter its critical section at a time, the minimal excluding sets are the sets of  k+1 proceses
• By a mutually excluding set we mean any set of processes containing a minimal mutually excluding set
• A mutually nonexcluding set is a set of processes not containing any minimal mutually excluding set