… We establish that the infinite grid and the transition graphs of … the Kleene equality and we
present families of graphs in which … the free product of graphs to preserve the Kleene equality. …

… We define term graphs as special 2-pointed graphs by induction on the complexity of ground
… that we can include meet into the language of Kleene algebras without losing equality of …

… To extend the above graph-theoretical characterisation to Kleene allegories, we need to …
We perform a reduction from the equality of languages denoted by regular expressions with …

… is decidable: the problem reduces to the equality of the denoted regular languages. Putting
… setting where the above graphs are acyclic—and we show that the corresponding equational …

… over the syntax of Kleene lattices, that is to say without the … by identifying the output of the
first graph with the input of the … If e = f, we say that regular laws prove the equality of e and f, …

… Instead of transforming the graphs of the schemes directly, we … of Kleene’s theorem to construct
equivalent expressions in the … equality in this system; that is, equality in the free KAT over …

… ) ⊕ C 1 Ω , it is not hard to see that the graphs of θ i are closed, thus, the θ i are also continuous.
… continuous, we would have equality of the limits of the image-sequences (and this is not …

… We study one such structure on Kleene’s … the recursively enumerable sub-pca of the Graph
model, results differ as we can compute the (partial) complement function using the equality. …

… allegories and the equality of certain sets of graphs… the automaton model and establish the
Kleene theorem. In Chapter 4 we detail how this applies to Kleene allegories, and provide the …

… we need the symbol + for the join operation in the dioid … The next model we consider are
sets of paths in a graph. We … We now show that the right unfold law becomes an equality. …