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Review of "P. Jancar, F. Mraz, M. Platek & J. Vogel, Monotonicity of restarting automata, J. Autom. Lang. Combin. 12 (2007) 355-371"

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MR2436368 (2009k:68123) 68Q45 (68Q42)

Janˇcar, Petr (CZ-TUO-C);Mr´az, Frantiˇsek (CZ-KARL-CS); Pl´atek, Martin (CZ-KARL-CS);Vogel, J¨org (D-FSU-II)

Monotonicity of restarting automata. (English summary) J. Autom. Lang. Comb.12 (2007),no. 3,355–371.

A restarting automaton is like a nondeterministic linear bounded automaton but it may remove tape cells. It moves its head, which is provided with a look-ahead scanning window of fixed length, to the right: it can rewrite the content of the window by a shorter word, and it can restart (move the head to the leftmost cell and enter the initial state). Restarting automata may also be viewed as a special type of regulated, length-reducing rewriting system, and in that sense they are applied in analyzing sentences of natural languages; they provide stepwise simplifications of a given sentence while the (in)correctness of the sentence is not affected.

This paper deals with several types of these automata as well as (strict) monotonicity proper-ties imposed upon their computations. The many resulting language families are compared with respect to their generating power; some families coincide with the context-free languages. Fi-nally, the (un)decidability of some monotonicity properties is established for the respective types of restarting automata.

Reviewed byPeter R. J. Asveld

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