Shuffle languages, Petri nets, and context-sensitive grammars

Flow expressions have been proposed as an extension of the regular expressions designed to model concurrency. We examine a simplification of these flow expressions which we call shuffle expressions. We introduce two types of machines to aid in recognizing shuffle languages and show that one such machine may be equivalent to a Petri Net. In addition, closure and containment properties of the related language classes are investigated, and we show that one machine type recognizes at least a restricted class of shuffle languages. Finally, grammars for all shuffle languages are generated, and the shuffle languages are shown to be context-sensitive.

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