Jumping Grammars and Discontinuous Computation
Indisputably, processing information in a largely discontinuous way has become a quite common computational phenomenon [BYRN11, BCC10, MRS08]. Indeed, consider a process p that deals with information i. During a single computational step, p can read a piece of information x in i, erase it, generate a new piece of information y, and insert y into i possibly far away from the original occurrence of x, which was erased. Therefore, intuitively speaking, during its computation, p keeps jumping across i as a whole. To explore computation like this systematically and rigorously, the language theory should provide computer science with language-generating models to explore various information processors mathematically, so it should do so for the purpose sketched above, too.
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