Undecidability of finite convergence for concatenation, insertion and bounded shuffle operators

Abstract

The k-insertion and shuffle operations on formal languages have been extensively studied in the computer science and control systems literature. These operations can be viewed as purely abstract, as representations of biological processes or as models of the interleavings of concurrent processes. Questions naturally arise about closure and decidability. Many have been previously answered, especially as regards closure and non-closure of these operations on regular and context free languages. Here we will show the undecidability of a number of problems concerning the interaction of regular and context free languages under insertion and bounded shuffle, and the interaction of context free languages under self insertion and self bounded shuffle. Most of these proofs are consequences of the fact that the problem to decide if a Turing machine has an upper limit on execution time, independent of input, is undecidable.

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Cite this paper

@inproceedings{Hughes2005UndecidabilityOF, title={Undecidability of finite convergence for concatenation, insertion and bounded shuffle operators}, author={Charles E. Hughes}, year={2005} }