Geodesic
On the recognition of the tautological nature of propositional formulas
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VII, Tome 60 (1976), pp. 197-206

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A formal language whose propositions express (in some sense) the properties of propositional formulas is described in the paper. For a certain subset of propositions of this language it is proved that each of them defines a class of propositional formulas, on which it is possible to recognize the tautological nature in a time polynomially dependent on the formula's length. 
@article{ZNSL_1976_60_a14,
     author = {P. Yu. Suvorov},
     title = {On the recognition of the tautological nature of propositional formulas},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {197--206},
     publisher = {mathdoc},
     volume = {60},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_60_a14/}
}
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P. Yu. Suvorov. On the recognition of the tautological nature of propositional formulas. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VII, Tome 60 (1976), pp. 197-206. http://geodesic.mathdoc.fr/item/ZNSL_1976_60_a14/