Finding shuffle words that represent optimal scheduling of shared memory access

In the present paper, we introduce and study the problem of computing, for any given nite set of words, a shu e word with a minimum so-called scope coincidence degree. The scope coincidence degree is the maximum number of di erent symbols that parenthesise any position in the shu e word. This problem is motivated by an application of a new automaton model and can be regarded as the problem of scheduling shared memory accesses of some parallel processes in a way that minimises the number of memory cells required. We investigate the complexity of this problem and show that it can be solved in polynomial time.