Syntactic and semantic aspects of parallelism
We define and investigate new methods for the parallel composition of words and languages. The operation of parallel composition leads to new shuffle-like operations defined by syntactic constraints on the usual shuffle operation. The approach is applicable to concurrency, providing a method to define the parallel composition of processes. It is also applicable to parallel computation.
The syntactic constraints are introduced using a uniform method based on the notion of a trajectory. We obtain in a natural way a large class of semirings.
The approach is amazingly flexible. Diverse concepts from the theory of concurrency can be introduced and studied in this framework. For instance, we provide examples of applications to the fairness property and parallelization of non-context-free languages in terms of context-free and even regular languages.
Semantic constraints mean constraints applied to the symbols (atomic actions) that occur inside of processes. Such constraints provide methods to define the parallel composition of processes that have critical sections, priorities or re-entrant routines. They are also applicable for modelling the communication between processes.
KeywordsCritical Section Regular Language Finite Automaton Parallel Composition Semantic Constraint
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