Shuffle languages, Petri nets, and context-sensitive grammars

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Abstract
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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