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We introduce finite-state verification techniques for the π-calculus whose design and correctness are justified coalgebraically. In particular, we formally specify and implement a minimization algorithm for HD-automata derived from π-calculus agents. The algorithm is a generalization of the partition refinement algorithm for classical automata and is specified as a coalgebraic construction defined using λ→, Φ, Σ, a polymorphic λ-calculus with dependent types. The convergence of the algorithm is proved; moreover, the correspondence of the specification and the implementation is shown.