Abstract. This paper describes the architecture of a toolkit, called Mihda, providing facilities to minimise labelled transition systems for name passing calculi. The structure of the toolkit is derived from the co-algebraic formulation of the partition-refinement minimisation algorithm for HD-automata. HD-automata have been specifically designed to allocate and garbage collect names and they provide faithful finite state representations of the behaviours of π-calculus processes. The direct correspondence between the coalgebraic specification and the implementation structure facilitates the proof of correctness of the implementation. We evaluate the usefulness of Mihda in practise by performing finite state verification of π-calculus specifications. 1

Inspired from the recent developments in theories of non-wellfounded syntax (coinductively defined languages) and of syntax with binding operators, the structure of algebras of wellfounded and non-wellfounded terms is studied for a very general notion of signature permitting both simple variable binding operators as well as operators of explicit substitution. This is done in an extensional mathematical setting of initial algebras and final coalgebras of endofunctors on a functor category. In the non-wellfounded case, the fundamental operation of substitution is more beneficially defined in terms of primitive corecursion than coiteration.