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Self doubts

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Whether the equality of DPDA is decidable or undecidable?
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it will be decidable because it is similar to membership algorithm. two automata is said be equal if they accept same language .let M1 accept language L1 and M2 accept language L2 then we have to check whether L1 is member of M2 or not or whether L2 is member of M1 or not.since membership algorithm for DCFL is decidable so the equality of DPDA will be decidable.
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