Tree automata modulo associativity and commutativity axioms, called AC tree automata, accept trees by iterating the transition modulo equational reasoning. The class of languages accepted by monotone AC tree automata is known to include the solution set of the inequality x × y > z, which implies that the class properly includes the AC closure of regular tree languages. In the paper, we characte...

There are many decision problems in automata theory (including membership, emptiness, emptiness of intersection, inclusion and universality problems) that for some classes of tree automata are NP-hard. The study of their parameterized complexity allows us to find new bounds of their non-polynomial time algorithmic behaviors. We present results of such a study for classical tree automata (TA), r...

in this paper, we define the concepts of a complex fuzzy subset and a complex fuzzy finite state automaton. then we extend the notion of a complex fuzzy finite state automaton and introduce the notion of a general complex fuzzy automaton. after that we define the concept of a max- min general complex fuzzy automaton and construct some equivalence relations and some congruence relations in a max...

Tree automata based algorithms are essential in many fields in computer science such as verification, specification, program analysis. They become also essential for databases with the development of standards such as XML. In this paper, we define new classes of non deterministic tree automata, namely residual finite tree automata (RFTA). In the bottom-up case, we obtain a new characterization ...

A new tree automata framework, called equational tree automata, is presented. In the newly introduced setting, congruence closures of recognizable tree languages are recognizable. Furthermore, we prove that in certain useful cases, recognizable tree languages are closed under union and intersection. To compare with early related work, e.g. [7], we discuss the relationship between linear bounded...

Automata-based methods have been successfully employed to prove tight complexity bounds for reasoning in many classical logics, and in particular in Description Logics (DLs). Very recently, the ideas behind these automata-based approaches were adapted for reasoning also in fuzzy extensions of DLs, with semantics based either on finitely many truth degrees or the Gödel t-norm over the interval [...

We introduce symbolic tree automata as a generalization of finite tree automata with a parametric alphabet over any given background theory. We show that symbolic tree automata are closed under Boolean operations, and that the operations are effectively uniform in the given alphabet theory. This generalizes the corresponding classical properties known for finite tree automata.

We introduce various types of w-automata, top-down automata and bottom-up automata on infinite trees. We study the power of deterministic and nondeter-ministic tree automata and prove that deterministic and non-deterministic bottom-up tree automata accept the same intinite tree sets. We establish a relationship between tree automata, Logic programs, recursive program schemes, and the monadic se...

We study three notions of directability of fuzzy automata akin to the D1-, D2and D3-directability of nondeterministic automata. Thus an input word w of a fuzzy automaton is D1-directing if a fixed single state is reachable by w from all states, D2-directing if exactly the same states are reachable by w from every state, and D3-directing if there is a state reachable by w from every state. We st...

the purpose of the present work is to introduce the concept of bifuzzy core of a fuzzy automaton, which induces a bifuzzy topology on the state-set of this fuzzy automaton. this is shown that this bifuzzy topology can be used to characterize the concepts such as bifuzzy family of submachines, bifuzzy separable family and bifuzzy retrievable family of a fuzzy automaton.