Density of Tautologies in Logics with One Variable

@article{Aszals2012DensityOT,
  title={Density of Tautologies in Logics with One Variable},
  author={L{\'a}szl{\'o} Aszal{\'o}s and Tam{\'a}s Herendi},
  journal={Acta Cybern.},
  year={2012},
  volume={20},
  pages={385-398}
}
In the present paper we estimate the ratio of the number of tautologies and the number of formulae of length n by determining the asymptotic density of tautologies in different kinds of logics with one variable. The logics under consideration are the ones with a single connective (nand or nor); negation with a connective (disjunction or conjunction); and several connectives. 
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Computing the density of tautologies in propositional logic by solving system of quadratic equations of generating functions

A fundamental relation between generating functions' values on the singularity point and ratios of coefficients is discovered, which can be understood as another intepretation of the Szegő lemma for certain quadratic systems.

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