Abstract

An operation M* which constructs from a given structure M a tree-like structure whose domain consists of the finite sequences of elements of M is considered. A notion of automata running on such tree-like structures is defined. It is shown that automata of this kind characterise expressive power of monadic second order logic (MSOL) over tree-like structures. Using this characterisation it is proved that MSOL theory of tree-like structures is effectively reducible to that of the original structures. As another application of the characterisation it is shown that MSOL on trees of arbitrary degree is equivalent to first order logic extended with unary least fixpoint operator.

Citations