The laterality problem for non-erasing Turing machines on {0,1} is completely solved
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 31 (1997) no. 2, pp. 159-204. 
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     author = {Margenstern, Maurice},
     title = {The laterality problem for non-erasing {Turing} machines on $\lbrace 0,1\rbrace $ is completely solved},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {159--204},
     publisher = {EDP-Sciences},
     volume = {31},
     number = {2},
     year = {1997},
     mrnumber = {1462585},
     zbl = {0878.68063},
     language = {en},
     url = {http://archive.numdam.org/item/ITA_1997__31_2_159_0/}
}
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Margenstern, Maurice. The laterality problem for non-erasing Turing machines on $\lbrace 0,1\rbrace $ is completely solved. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 31 (1997) no. 2, pp. 159-204. http://archive.numdam.org/item/ITA_1997__31_2_159_0/

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