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...

1 Fa ulty of Mathemati s, Informati s, and Me hani s Warsaw University, Poland E-mail address: {shummel,henrykm,niwinski} mimuw.edu.pl Abstra t. The game tree languages an be viewed as an automata-theoreti ounterpart of parity games on graphs. They witness the stri tness of the index hierar hy of alternating tree automata, as well as the xed-point hierar hy over binary trees. We onsider a game ...

It is well known that for a regular tree language it decidable whether or not can be recognized by deterministic top-down automaton (DTA). However, the computational complexity of this problem has been studied. We show given bottom-up decided in quadratic time its DTA. Since there are finite languages cannot DTAs, we also consider unions DTAs and here, definability within automata time.

When reading an input tree, a bottom-up tree automaton is \unaware" of where it is relative to the root. This problem is important to the eecient implementation of decision procedures for the Monadic Second-order Logic (M2L) on nite trees. In 7], it is shown how exponential state space blow-ups may occur in common situations. The analysis of the problem leads to the notion of guided tree automa...

We study the state complexity of regular tree languages for tree matching problem. Given a tree t and a set of pattern trees L, we can decide whether or not there exists a subtree occurrence of trees in L from the tree t by considering the new language L′ which accepts all trees containing trees in L as subtrees. We consider the case when we are given a set of pattern trees as a regular tree la...

We identify the class of Σ1–inductive sets studied by Moschovakis as a set theoretical generalization of the class (1, 3) of the Rabin-Mostowski index hierarchy of alternating automata on infinite trees. That is, we show that every tree language recognized by an alternating automaton of index (1, 3) is Σ1–inductive, and exhibit an automaton whose language is complete in this class w.r.t. contin...

This paper introduces a machinery called attributed top-down parsing automaton which performs top{down parsing of strings and, simultaneously, the evaluation of arbitrary noncircular attribute grammars. The strategy of the machinery is based on a single depth{ rst left{to{right traversal over the syntax tree. There is no need to traverse parts of the syntax tree more than once, and hence, the s...