Merging regular processes by means of fixed-point theory
First, we investigate a trace-set semantics of processes with \(\mu\)- recursion and arbitrary interleaving (merge). \(\mu\)-recursion is the analogue of recursion in standard programming by means of a recursive procedure. Iteration using while-statements can be viewed as a special case of this: so-called regular recursion. The semantics is used to support a formalism that determines the merge of two regular sequential (nondeterministic) processes. Next, we turn to processes with merge, \(\mu\)-recursion, and a second kind of recursion, called \(\alpha\)- recursion. This kind of recursion when applied in a regular forms is the equivalent of the Kleene-star iteration known from formal language theory. It involves only arbitrary big, but finite numbers of iterations. A different, more complicated framework is needed to give meaning to this kind of processes. Hereafter we define the semantics of the fair merge of these processes. Finally, we use this to prove the correctness of a formalism similar to the one for arbitrary merge in order to calculate the fair merge of two regular sequential (nondeterministic) processes with \(\mu\)-recursion.
scientific article; zbMATH DE number 3972176
scientific article