Machines in closed categories in general and in categories of heyting Algebra valued sets in particular

• Main Author: Monserrat Antich, Miquel
• Format: Others
• Language: en
• Published: McGill University 1990
• Subjects: Mathematics.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=59807

A survey of the minimal realization theory of Arbib and Manes for "state-behavior" machines in a category is given, and how the closed category machines of Goguen are included in the above machines is discussed in detail. A survey of the non-deterministic treatment due to Arbib and Manes is given. A study of C-machines in a closed category for a monoid C is given in both the deterministic and the non-deterministic cases. A notion of u-machine in a topos for a morphism of monoids u is introduced and studied. A discussion of the category of H-valued sets as a topos is given and finally some of the concepts of automata theory for the deterministic case are investigated in this context, regarding the category of H-valued sets as a closed category and especially when H is a finite chain.