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We consider the sabotage game as presented by van Ben-them. In this game one player moves along the edges of a finite multi-graph and the other player takes out a link after each step. One can consider usual algorithmic tasks like reachability, Hamilton path, or complete search as winning conditions for this game. As the game definitely ends after at most… (More)

We extend the propositional dynamic logic PDL of Fischer and Ladner with a restricted kind of recursive programs using the formalism of visibly pushdown automata (Alur, Madhusudan 2004). We show that the satisfiability problem for this extension remains decidable, gen-eralising known decidability results for extensions of PDL by non-regular programs.

We investigate bottom-up and top-down deterministic au-tomata on unranked trees. We show that for an appropriate definition of bottom-up deterministic automata it is possible to minimize the number of states efficiently and to obtain a unique canonical representative of the accepted tree language. For top-down deterministic automata it is well known that… (More)

We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic second-order (WMSO) formulas with free set variables. They transform a given structure into a structure with a domain consisting of finite sets of elements of the orignal structure. The definition of these… (More)

Given a Rabin tree-language and natural numbers i, j, the language is said to be i, j-feasible if it is accepted by a parity automaton using priorities {i, i+1, ..., j}. The i, j-feasibility induces a hierarchy over the Rabin-tree languages called the Mostowski hierarchy. In this paper we prove that the problem of deciding if a language is i, j-feasible is… (More)

We propose an extension of the tree automata with constraints between direct subtrees (Bogaert and Tison, 1992) to unranked trees. Our approach uses MSO-formulas to capture the possibility of comparing unboundedly many direct subtrees. Our main result is that the nonemptiness problem for the deterministic automata, as in the ranked setting, is decidable.… (More)

In this paper we lift the result of Hashiguchi of decidability of the restricted star-height problem for words to the level of finite trees. Formally, we show that it is decidable, given a regular tree language L and a natural number k whether L can be described by a disjunctive µ-calculus formula with at most k nesting of fixpoints. We show the same result… (More)

We continue the study of bottom-up unranked tree automata with equality and dis-equality constraints between direct subtrees. In particular, we show that the emptiness problem for the nondeterministic automata is decidable. In addition, we show that the universality problem, in contrast, is undecidable.

- Christof Löding
- 2001

We analyze the minimization problem for deterministic weak automata, a subclass of deterministic Büchi automata, which recognize the regular languages that are recognizable by deterministic Büchi and deterministic co-Büchi automata. We reduce the problem to the minimization of finite automata on finite words and obtain an algorithm running in time O(n · log… (More)