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GENERATION AND ANALYSIS OF FINITE MONOIDS WITH AN EMPHASIS ON SYNTACTIC MONOIDS

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This thesis by Bhavana Ajanahalli Raghupathi focuses on the generation and analysis of finite monoids, particularly syntactic monoids, within the context of computer science. It aims to create a database of syntactic monoids derived from regular state graphs with 2 to 5 states, exploring their algebraic properties and relationships to counter-free automata. The work includes code for generating these monoids, identifying key properties such as left zero, right zero, commutativity, dead states, and immortal states. The findings contribute to understanding finite monoids' relevance in computational theory and provide a foundation for future research.

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What is the difference between a group and a monoid?

ing to John Baez, a monad can be considered at least in two ways: A monad as a generalized monoid; this is clear since a monad is a monoid in a certain category, A monad as a tool for studying algebraic gadgets; for example, a group can be described by a certain monad.

What is monoid with an example?

In abstract algebra, a branch of mathematics, a monoid is a set equipped with an associative binary operation and an identity element. For example, the nonnegative integers with addition form a monoid, the identity element being 0. Algebraic structures between magmas and groups.