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Stochastic Semantics

Bozapalidis S., Rahonis G.

Fundamenta Informaticae

2017

Vol. 150, nr 2

143--177

We consider stochastic systems of equations of tree series, i.e., systems of equations whose right-hand sides are stochastic tree polynomials. We obtain their least solutions in arbitrary substochastic algebras, using both the [IO]- and OI-substitution mode. In the term algebra, we show that the consistency problem of the least [IO]- and OI-solutions is decidable, by reducing it to the consistency problem of stochastic context-free grammars. We prove a Kleene type theorem for the components of the least OI-solutions. The folklore Mezei-Wright result stating the coincidence of the components of least OI-solutions and behaviors of tree automata fails in the stochastic setup. As an application of our theory, we prove a Kleene theorem for the class of series generated by stochastic context-free grammars.

Multi-Valued MSO Logics Over Words and Trees

Droste M., Kuich W., Rahonis G.

Fundamenta Informaticae

2008

Vol. 84, nr 3-4

305-327

We introduce multi-valued Büchi and Muller automata over distributive lattices and a multi-valued MSO logic for infinite words. For this logic, we prove the expressive equivalence of w-recognizable and MSO-definable infinitary formal power series over distributive lattices with negation function. Then we consider multi-valued Muller tree automata and a multi-valued MSO logic for trees over distributive lattices. For this logic, we establish a version of Rabin's theorem for infinitary tree series.

On the size of stack and synchronization alphabets of tree automata

Rahonis G., Salomaa K.

Fundamenta Informaticae

1998

Vol. 36, nr 1

57-69

We consider classes of forests defined by synchronized and pushdown tree automata having a fixed size of , respectively, synchronization or pushdown alphabet. We show that such families have nice properties, for instance, they from either a sheaf or a strict alphabetic cone of forests. Furthermore, for the (deterministic and nondeterministic) synchronized tree automata and the real-time pushdown tree automata we obtain a strict infinite forest hierarchy with respect to the alphabet size.