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We extend the binary search technique to searching in trees. We consider two models of queries: questions about vertices and questions about edges. We present a general approach to this sort of problem , and apply it to both cases, achieving algorithms constructing optimal decision trees. In the edge query model the problem is identical to the problem of(More)
We show that deterministic collapsible pushdown automata of second level can recognize a language which is not recognizable by any deterministic higher order pushdown automaton (without collapse) of any level. This implies that there exists a tree generated by a second level collapsible pushdown system (equivalently: by a recursion scheme of second level),(More)
We show that collapsible deterministic second level pushdown automata can recognize more languages than deterministic second level pushdown automata (without collapse). This implies that there exists a tree generated by a second level recursion scheme which is not generated by any second level safe recursion scheme. 1 Introduction In verification we often(More)
We present a pumping lemma for the class of ε-contractions of pushdown graphs of level n, for each n. A pumping lemma was proposed by Blumensath, but there is an irrecoverable error in his proof; we present a new proof. Our pumping lemma also improves the bounds given in the invalid paper of Blumensath. 1 Introduction Higher-order pushdown systems are a(More)
Alternating timed automata on infinite words are considered. The main result is a characterization of acceptance conditions for which the emptiness problem for the automata is decidable. This result implies new decidability results for fragments of timed temporal logics. It is also shown that, unlike for MITL, the characterisation remains the same even if(More)
Regular cost functions provide a quantitative extension of regular languages that retains most of their important properties, such as expressive power and decidability, at least over finite and infinite words and over finite trees. Much less is known over infinite trees. We consider cost functions over infinite trees defined by an extension of weak monadic(More)