The n-ary initial literal and literal shuffle

The literal and initial literal shuffle operations were introduced to model the synchronization of two processes. However, due to their non-associative nature, they are inadequate for modeling the synchronization of multiple processes. In this work, we extend both operations to $n$-ary versions, enabling the modeling of multiple synchronized processes. We also introduce “iterated” variants of these $n$-ary shuffles, which differ from previously proposed iterated versions for the two-argument cases. We investigate formal properties and demonstrate that in a full trio their expressive power coincides with that of the general shuffle operation. Furthermore, we examine closure properties and explore various decision problems inspired by analogous problems for the general shuffle operation. For instance, determining whether a word belongs to the $n$-ary initial literal shuffle of $n$ words is a decision problem in L, whereas the corresponding problem for the $n$-ary literal shuffle is NP-complete.