In this paper, two different ways of introducing alternation for lattice-valued (referred to as {L}valued)  regular tree grammars and {L}valued top-down tree automata are compared. One is the way which defines the alternating regular tree grammar, i.e., alternation is governed by the non-terminals of the grammar and the other is the way which combines state with alternation. The first way is ta...

We show how alternating automata provide decision procedures for the equality of inductively de3ned Boolean functions and present applications to reasoning about parameterized families of circuits. We use alternating word automata to formalize families of linearly structured circuits and alternating tree automata to formalize families of tree structured circuits. We provide complexity bounds fo...

μ-Calculus and automata on infinite trees are complementary ways of describing infinite tree languages. The correspondence between μ-Calculus and alternating tree automaton is used to solve the satisfiability and model checking problems by compiling the modal μ-Calculus formula into an alternating tree automata. Thus advocating an automaton model specially tailored for working with modal μ-Calc...

μ-Calculus and automata on infinite trees are complementary ways of describing infinite tree languages. The correspondence between μ-Calculus and alternating tree automaton is used to solve the satisfiability and model checking problems by compiling the modal μ-Calculus formula into an alternating tree automata. Thus advocating an automaton model specially tailored for working with modal μ-Calc...

The nonemptiness problem for nondeterministic automata on infinite words can be reduced to a sequence of reachability queries. The length of a shortest witness to the nonemptiness is then polynomial in the automaton. Nonemptiness algorithms for alternating automata translate them to nondeterministic automata. The exponential blow-up that the translation involves is justified by lower bounds for...

Macro tree transducers (mtt) are an important model that both covers many useful XML transformations and allows decidable exact typechecking. This paper reports our first step toward an implementation of mtt typechecker that has a practical efficiency. Our approach is to represent an input type obtained from a backward inference as an alternating tree automaton, in a style similar to Tozawa’s X...

Distributed games, as defined in [6], is a recent multiplayer extension of discrete two player infinite games. The main motivation for their introduction is that they provide an abstract framework for distributed synthesis problems, in which most known decidable cases can be encoded and solved uniformly. In the present paper, we show that this unifying approach allows as well a better understan...

We introduce a new kind of tree automaton, a dependency tree automaton, that is suitable for deciding properties of classes of terms with binding. Two kinds of such automaton are defined, nondeterministic and alternating. We show that the nondeterministic automata have a decidable nonemptiness problem and leave as an open question whether this is true for the alternating version. The families o...

We introduce a new kind of tree automaton, a dependency tree automaton, that is suitable for deciding properties of classes of terms with binding. Two kinds of such automaton are defined, nondeterministic and alternating. We show that the nondeterministic automata have a decidable nonemptiness problem and leave as an open question whether this is true for the alternating version. The families o...

We show that a tree language recognized by a deterministic parity automaton is either hard for the co–Büchi level and therefore cannot be recognized by a weak alternating automaton, or is on a very low level in the hierarchy of weak alternating automata. A topological counterpart of this property is that a deterministic tree language is either Π 1 complete (and hence non Borel), or it is on the...