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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)
We introduce ICE, a robust learning paradigm for synthesizing invari-ants, that learns using examples, counterexamples , and implications, and show that it admits honest teachers and strongly convergent mechanisms for invariant synthesis. We observe that existing algorithms for black-box abstract interpretation can be interpreted as ICE-learning algorithms.(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 consider the transition graphs of regular ground tree (or term) rewriting systems. The vertex set of such a graph is a (possibly infinite) set of trees. Thus, with a finite tree automaton one can represent a regular set of vertices. It is known that the backward closure of sets of vertices under the rewriting relation preserves regularity, i.e., for a(More)