POS Tagging - Hidden Markov Model

What is the primary purpose of Part-of-Speech (POS) tagging in natural language processing?
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In a Hidden Markov Model, what are the 'hidden' states?
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What does the word 'Markov' refer to in Hidden Markov Models?
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What are emission probabilities in an HMM for POS tagging?
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Why is context important in POS tagging?
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In the calculation P(tag₂|tag₁) = count(tag₁, tag₂) / count(tag₁), what does this represent?
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What is the main advantage of using statistical methods like HMMs over hand-crafted rules for POS tagging?
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In the Viterbi algorithm, what does dynamic programming help achieve?
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What is a major limitation of first-order HMMs for POS tagging?
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