Toward a Uniform Theory of Effectful State Machines

The countable valuation monad, the countable distribution monad, and the countable subdistribution monad are often used in the coalgebraic treatment of discrete probabilistic transition systems. We identify preorders on them using a technique based on ...

For deterministic systems, expressed as coalgebras over polynomial functors, every tree t (an element of the final coalgebra) turns out to represent a new coalgebra A_t. The universal property of this family of coalgebras, resembling freeness, is that ...

For each regular language L we describe a family of canonical nondeterministic acceptors (nfas). Their construction follows a uniform recipe: build the minimal dfa for L in a locally finite variety V , and apply an equivalence between the category of ...