Geodesic
Kolmogoroff algorithms are stronger than turing machines
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VII, Tome 60 (1976), pp. 29-37

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A predicate is constructed which is recognizable in real time by a Kolmogoroff algorithm but which is not recognizable in real time by a machine with polynomial accessibility. 
@article{ZNSL_1976_60_a2,
     author = {D. Yu. Grigor'ev},
     title = {Kolmogoroff algorithms are stronger than turing machines},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {29--37},
     publisher = {mathdoc},
     volume = {60},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_60_a2/}
}
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D. Yu. Grigor'ev. Kolmogoroff algorithms are stronger than turing machines. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VII, Tome 60 (1976), pp. 29-37. http://geodesic.mathdoc.fr/item/ZNSL_1976_60_a2/