A Logical Characterization of Systolic Languages

In this paper we study, in the framework of mathematical logic, L(SBTA) i.e. the class of languages accepted by Systolic Binary Tree Automata. We set a correspondence (in the style of B uchi Theorem for regular languages) between L(SBTA) and MSOSig], i.e. a decid-able Monadic Second Order logic over a suitable innnite signature Sig. We also introduce a natural subclass of L(SBTA) which still properly contains the class of regular languages and which is proved to be characterized by Monadic Second Order logic over a nite signature Sig 0 Sig. Finally, in the style of McNaughton Theorem for star free regular languages , we introduce an expression language which precisely denotes the class of languages deened by the rst order fragment of MSOSig 0 ].