ace test series

Question

Number of equivalence classes w.r.t language,

L={(a^n)(b^n)(c^n)| n>=0} is

answer:infinity

explain why?

Comments

this is a equivalence  problem hence undecidable i think that's why they use infinity

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also there is a theorem: a language is regular iff number of myhill nerode equivalence class is finite.

so neither this language is regular, and hence nor is its myhill nerode equivalence class should be finite.

Answer 1

The meaning of equivalence classes from Myhill Nerode Theorem is the no of states in the minimal dfa.

Given:Number of equivalence classes w.r.t language,
L={(a^n)(b^n)(c^n)| n>=0} is

First of all the dfa will contain infinite states because no dfa is possible as it is not a regular language .. what they mean possibly is that they will have states for all possible values of n ranging fromm 0 to infinity and thus the dfa will contain infinite states.

Comments

Thanks anjali

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for further refernce:https://gateoverflow.in/29550/toc-number-of-equivalence-classes refer this