Timed systems, such as timed automata, are usually analyzed using their operational semantics on timed words. The classical region abstraction for timed automata reduces them to (untimed) finite state automata with the same time-abstract properties, such as state reachability. We propose a new technique to analyze such timed systems using finite tree automata instead of finite word automata. Th...

This paper grew out of three tutorial lectures on automatic structures given at the Logic Colloquium 2007 in Wroc law (Poland). The paper will follow the outline of the tutorial lectures, supplementing some material along the way. We discuss variants of automatic structures related to several models of computation: word automata, tree automata, Büchi automata, and Rabin automata. Word automata ...

2 From Modal -Calculus to Alternating Tree Automata 4 2.1 Modal -Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 Kripke Structures . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.3 Substitution . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.4 Semantics . . . . . . . . . . . . . . . . . . . . . ....

We observe that pushdown tree automata (PTAs) known in the literature cannot express combinations of branching and pushdown properties. This is because a PTA processes the children of a tree node in possibly different control states but with identical stacks. We propose branching pushdown tree automata (BPTAs) as a solution. In a BPTA, a push-move views its matching pops as an unbounded, unorde...