Annotated pushdown automata provide an automaton model of higher-order recursion schemes, which may in turn be used to model higher-order programs for the purposes of verification. We study Ground Annotated Stack Tree Rewrite Systems – a tree rewrite system where each node is labelled by the configuration of an annotated pushdown automaton. This allows the modelling of fork and join constructs ...

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 ...

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...

The model-checking problem for higher-order recursive programs, expressed as higher-order recursion schemes (HORS), and where properties are specified in monadic second-order logic (MSO) has received much attention since it was proven decidable by Ong ten years ago. Every HORS may be understood as a simply-typed λ-term G with fixpoint operators Y whose free variables a, b, c . . . ∈ Σ are of or...

A non-deterministic automaton running on infinite trees is unambiguous if it has at most one accepting run on every tree. The class of languages recognisable by unambiguous tree automata is still not well-understood. In particular, decidability of the problem whether a given language is recognisable by some unambiguous automaton is open. Moreover, there are no known upper bounds on the descript...

A non-deterministic automaton running on infinite trees is unambiguous if it has at most one accepting run on every tree. The class of languages recognisable by unambiguous tree automata is still not well-understood. In particular, decidability of the problem whether a given language is recognisable by some unambiguous automaton is open. Moreover, there are no known upper bounds on the descript...

We extend the automata-theoretic framework for reasoning about infinitestate sequential systems to handle also the global model-checking problem. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Chec...

In this paper we introduce a sub-family of synchronized alternating pushdown automata, one-turn Synchronized Alternating Pushdown Automata, which accept the same class of languages as those generated by Linear Conjunctive Grammars. This equivalence is analogues to the classical equivalence between one-turn PDA and Linear Grammars, thus strengthening the claim of Synchronized Alternating Pushdow...

We consider infinite two-player games on pushdown graphs. For parity winning conditions, we show that the set of winning positions of each player is regular and we give an effective construction of an alternating automaton recognizing it. This provides a DEXPTIME procedure to decide whether a position is winning for a given player. Finally, using the same methods, we show, for any ω-regular win...

In this paper we introduce a variant of alternating pushdown automata, Synchronized Alternating Pushdown Automata, which accept the same class of languages as those generated by conjunctive grammars.