Minimal Sequential Interaction Machines

Persistent Turing Machines PTMs are an abstract model for sequential interactive comput ing marrying coinductive semantics with e ective constructibility They are multitape machines with work tape contents preserved between interactions whose behavior is characterized obser vationally by input output streams Notions of PTM equivalence and expressiveness have been studied proving that in non algorithmic environments they are more expressive than TMs However the question of minimal or canonical PTMs has not been addressed until now In this work minimal PTMs are de ned based on the notion of PTM state equivalence It is shown that there exists a homomorphism between any PTM and its minimal form and that all equiv alent minimal PTMs are isomorphic Minimal PTMs can be represented by nal coalgebras con rming the coinductive nature of the foundations of interactive computing