Logical definability of Y-tree and trellis systolic É -languages1

 Monti Angelo 2 and Peron Adriano 3

Abstract:

 In this paper we investigate the correspondence (in the style of the well known Büchi Theorem) between É-languages accepted by systolic automata and suitable (proper) extensions of the Monadic Second Order theory of one successor ( MSO [<] ). To this purpose we extend Y -tree and trellis systolic automata to deal with É-words and we study the expressiveness, closure and decidability properties of the two classes of É-languages accepted by Y -tree and trellis automata, respectively. We define, then, two extensions of , MSO [<], MSO [<, adj ] and MSO [<, 2x] , which allow to express Y -tree É-languages and trellis É-languages, respectively.

Footnotes

  1 Research partially supported by MURST Progetto Cofinanziato TOSCA. 2 Dipartimento Scienze dell'Informazione, Universitŕ di Roma (La Sapienza), 00198, Via Salaria 113, Italy, e-mail: monti@dsi.uniroma1.it 3 Dipartimento di Matematica e Informatica, Universitŕ di Udine, 33100, Via Zanon 6, Italy, e-mail: peron@dimi.uniud.it