As already 2-monotone R-automata accept NP-complete languages, we introduce a restricted variant of -monotonicity for restarting automata, called sequential -monotonicity. For restarting automata without auxiliary symbols, this restricted variant still yields infinite hierarchies. However, for restarting automata with auxiliary symbols, all degrees of sequential monotonicity collapse to the first level, implying that RLWW-automata that are sequentially monotone of degree for any only accept context-free languages.
@article{ITA_2007__41_2_157_0,
author = {Jurdzi\'nski, Tomasz and Otto, Friedrich},
title = {Sequential monotonicity for restarting automata},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
volume = {41},
year = {2007},
pages = {157-175},
doi = {10.1051/ita:2007013},
mrnumber = {2350642},
zbl = {pre05235506},
language = {en},
url = {http://dml.mathdoc.fr/item/ITA_2007__41_2_157_0}
}
Jurdziński, Tomasz; Otto, Friedrich. Sequential monotonicity for restarting automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) pp. 157-175. doi : 10.1051/ita:2007013. http://gdmltest.u-ga.fr/item/ITA_2007__41_2_157_0/
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