Cayley graphs considered as language recognisers are as powerful as the more general finite state automata. This paper applies Cayley graphs to define a class of automata and describe minimal automata of this type, all their congruences and the Nerode equivalence of states. Throughout, the word graph means a finite directed graph without multiple edges but possibly with loops, and D = (V,E) is ...

We improve on an existing [P.A. Abdulla, J. Högberg, L. Kaati. Bisimulation Minimization of Tree Automata. Int. J. Found. Comput. Sci. 18(4): 699–713, 2007] bisimulation minimization algorithm for finite-state tree automata by introducing backward and forward bisimulation and developing minimization algorithms for them. Minimization via forward bisimulation is also effective on deterministic tr...

In this paperwe adapt thewell-knownBrzozowskideterminizationmethod to fuzzy automata. Thismethod gives better results than all previously knownmethods for determinization of fuzzy automata developed by Bělohlávek [InformSciences 143 (2002)205–209],Li andPedrycz [FuzzySet Syst 156 (2005)68–92], Ignjatović et al. [Inform Sciences 178 (2008) 164–180], and Jančić et al. [Inform Sciences 181 (2011) ...

Two examples of automata-theoretic models for the validation of xml documents against user-de ned schema are the stepwise unranked tree automaton (suta) and the parallel unranked tree automaton (puta). By adding a weight, taken from some semiring, to every transition we generalise these two qualitative automata models to quantitative models, thereby obtaining weighted stepwise unranked tree aut...

With every rational language we associate a canonical non-determinis-tic automaton, that subsumes all possible \minimal" automata recognizing this language.

We identify a new class of decidable hybrid automata: namely, parallel compositions of semi-algebraic o-minimal automata. The class we consider is fundamental to hierarchical modeling in many exemplar systems, both natural and engineered. Unfortunately, parallel composition, which is an atomic operator in such constructions, does not preserve the decidability of reachability. Luckily, this pape...

In this paper we present algorithms to compute finite state automata which, given any rational language, recognize the languages of normal words and n-chains. We also show how these automata can be used to compute the Hilbert series and Poincaré series for any algebra with a rational set of leading words of its minimal Gröbner basis.

We define compact automata and show that every language has a unique minimal compact automaton. We also define recognition of languages by compact left semitopological monoids and construct the analogue of the syntactic monoid in this context. For rational languages this reduces to the usual theory of finite automata and finite monoids.

We give a canonical representation for trim acyclic deterministic finite automata (ADFA) with n states over an alphabet of k symbols. Using this normal form, we present a backtracking algorithm for the exact generation of ADFAs. This algorithm is a non trivial adaptation of the algorithm for the exact generation of minimal acyclic deterministic finite automata (MADFA), presented by Almeida et al..

Innnite leaf alphabets provide a new approach to remove the connection between the sizes of the leaf alphabet and the set of states of a tree automaton. Unique minimal tree automata can be constructed for classes of tree automata; however, such a class cannot be nite.