The theory provides a condition for a language to be regular. It’s very much widely used to prove the fact that a language that is given is irregular. Consider a language L that could define a relation ML on strings by the rule x ML y, the number of states that accept L in its small automation is equal to number of equivalent classes in ML. The fact we should understand out of this statement is that the fact of finite automation has only finite number of states. That is any language which is described in this form should have the finite number of string patterns. Now this is expressed by right invariant relation with finite-index. A stronger prefix equivalence is a form this invariant relation. Three relevant statements include Relation ~L is with a finite index, L is acceptable by finite and deterministic automation and L is the union formed out of equivalence classes of the right invariant relation of the finite index. Let's discuss the topic in detail from the PowerPoint presentation.

Dency Varghese

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