We consider the state complexity of extensions of the Kleene star and quotient operations to unranked tree languages. Due to the nature of the tree structure, there are two distinct ways to define the star operation for trees, we call these operations, respectively, bottom-up and top-down star. We show that (n+ 3 2 )2 states are sufficient and necessary in the worst case to recognize the bottom...

We study the class of quasi-alphabetic relations, i.e., tree transformations de ned by tree bimorphisms (';L; ) with '; quasi-alphabetic tree homomorphisms and L a regular tree language. We present a canonical representation of these relations; as an immediate consequence, we get the closure under union. Also, we show that they are not closed under intersection and complement, and do not preser...

We prove that for a given deterministic top-down transducer with look-ahead it is decidable whether or not its translation definable (1) by linear tree (2) homomorphism. present algorithms construct equivalent such transducers if they exist.

Tree series transformations computed by bottom-up and top-down tree series transducers are called bottomup and top-down tree series transformations, respectively. (Functional) compositions of such transformations are investigated. It turns out that the class of bottom-up tree series transformations over a commutative and complete semiring is closed under left-composition with linear bottom-up t...

Alternating automata on infinite trees induce operations on languages which do not preserve natural equivalence relations, like having the same Mostowski–Rabin index, the same Borel rank, or being continuously reducible to each other (Wadge equivalence). In order to prevent this, alternation needs to be restricted to the choice of direction in the tree. For weak alternating automata with restri...

The logic called ATL (Alternating-time Temporal Logic) was introduced, in 1997, as a modal logic of agents. The first direct algorithm to test whether a given ATL-formula θ is satisfiable was provided by V. Goranko and G. van Drimmelen in 2006. Their algorithm is based on alternating infinite tree automata. In 2009, V. Goranko and D. Shkatov proposed a method to test satisfiability of a formula...

Letter to letter top-down tree transducers are investigated in this paper. Informally, trees which appear in the rules of such transducers are reduced to one letter in the right-hand side as in the left one. With an encoding of the tree transformations induced by such transducers into recognizable forests, we recently established the decidability of equivalence for linear top-down transducers. ...

A data tree is a tree whose every node carries a label from a finite alphabet and a datum from some infinite domain. We introduce a new model of automata over unranked data trees with a decidable emptiness problem. It is essentially a bottom-up alternating automaton with one register, enriched with epsilon-transitions that perform tests on the data values of the subtree. We show that it capture...

Hyper-minimization aims to reduce the size of the representation of a language beyond the limits imposed by classical minimization. To this end, the hyper-minimal representation can represent a language that has a finite difference to the original language. The first hyperminimization algorithm is presented for (bottom-up) deterministic tree automata, which represent the recognizable tree langu...