One of the prevailing ideas in applied concurrency theory and verification is the concept of automata minimization with respect to strong or weak bisimilarity. The minimal automata can be seen as canonical representations of the behaviour modulo the bisimilarity considered. Together with congruence results wrt. process algebraic operators, this can be exploited to alleviate the notorious state ...

We present a method to store additional information in a minimal automaton so that it is possible to compute a corresponding tree node number for a state. The number can then be used to retrieve additional information. The method works for minimal (and any other) deterministic acyclic finite state automata (DFAs). We also show how to compute the inverse mapping.

Partial words are sequences of characters from an alphabet in which some positions may be marked with a “hole” symbol, . We can create a -substitution mapping this symbol to a subset of the alphabet, so that applying such a substitution to a partial word results in a set of full words (ones without holes). This setup allows us to compress regular languages into smaller partial languages. Determ...

We show that for all n and α such that 1 ≤ n ≤ α ≤ 2 there is a minimal n-state nondeterministic finite automaton whose equivalent minimal deterministic automaton has exactly α states.

A result of Nicaud states that the number of distinct unary regular string languages recognized by minimal deterministic finite automata (DFAs) with n states is asymptotically equal to n2n−1. We consider the analogous question for symmetric difference automata (Z2NFAs), and show that precisely 22n−1 unary languages are recognized by n-state minimal Z2-NFAs.