Toward an Algebraic proof of Toda's theorem

• Main Author: Majlis, Flavia.
• Other Authors: Therien, D. (advisor)
• Format: Others
• Language: en
• Published: McGill University 2000
• Subjects: Mathematics.; Computer Science.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=30695

This thesis is devoted to an approach of computational complexity based on computations within finite semigroups. === The theory of finite semigroups and its algebraic aspects are deeply connected with the theory of automata and regular languages [Eil76a] [Pin86]. The link between finite monoids and regular languages, for instance, is well known. === We want to explore the existence of further links between a language that lies beyond the set of regular languages and the properties of the algebraic structure of the monoid recognizing it. The technique that will allow us to overcome the limitation of finite systems to recognize languages only within the set of regular languages is to approach a complexity class from the point of view of its leaf language [DPR92]. In this framework we expand the set of languages being contemplated by the model from the set of regular languages to the set PSPACE, the class of languages recognized by nondeterministic Turing machines in polynomial space. === We then classify a complexity class by analyzing the algebraic structure of the monoid recognizing its leaf language. === In this context, we will interpret a result by Toda [Tod91] in terms of the algebraic properties of the structure of the monoids recognizing the leaf languages of the classes involved.