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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 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)
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 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)
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)
Closed semi-algebraic sets in the plane form a powerful model of planar spatial datasets. We establish a characterization of the topological properties of such datasets expressible in the relational calculus with real polynomial constraints. The characterization is in the form of a query language that can only talk about points in the set and the "cones"(More)