DFC-algorithms for Suszko logic and one-to-one Gentzen type formalizations

We use here the notions and results from algebraic theory of programs in order to give a new proof of the decidability theorem for Suszko logic SCI (Theorem 3).We generalize the method used in the proof of that theorem in order to prove a more general fact that any prepositional logic which admits a cut-free Gentzen type formalization is decidable (Theorem 6).We establish also the relationship between the Suszko Logic SCI, one-to-one Gentzen type formalizations and deterministic and algorithmic regular languages (Remark 2 and Theorem 7, respectively).