Geodesic
A simplified proof of the real-time recognizability of palindromes on turing machines
Zapiski Nauchnykh Seminarov POMI, Theoretical application of methods of mathematical logic. Part II, Tome 68 (1977), pp. 123-139

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A comparatively short proof is given of the recognizability of palindromes in real time on multitape Turing machines. It is based on the same idea as the original proof by the author, and on Z. Galil's idea for simplifying the proof by using the Fischer–Paterson algorithm for finding all symmetric suffixes in linear time. 
@article{ZNSL_1977_68_a9,
     author = {A. O. Slisenko},
     title = {A simplified proof of the real-time recognizability of palindromes on turing machines},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {123--139},
     publisher = {mathdoc},
     volume = {68},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_68_a9/}
}
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A. O. Slisenko. A simplified proof of the real-time recognizability of palindromes on turing machines. Zapiski Nauchnykh Seminarov POMI, Theoretical application of methods of mathematical logic. Part II, Tome 68 (1977), pp. 123-139. http://geodesic.mathdoc.fr/item/ZNSL_1977_68_a9/