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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 consider a fragment of XPath where attribute values can only be tested for equality. We show that for any fixed unary query in this fragment, the set of nodes that satisfy the query can be calculated in time linear in the document size.

- Pawel Parys
- PODS
- 2009

We consider a fragment of XPath 1.0, where attribute and text values may be compared. We show that for any unary query in this fragment, the set of nodes that satisfy the query can be calculated in time linear in the document size and polynomial in the size of the query. The previous algorithm for this fragment also had linear data complexity but… (More)

- Pawel Parys
- LICS
- 2012

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 present a pumping lemma for each level of the collapsible pushdown graph hierarchy in analogy to the second author's pumping lemma for higher-order pushdown graphs (without collapse). Using this lemma, we give the first known examples that separate the levels of the collapsible pushdown graph hierarchy and of the collapsible pushdown tree hierarchy,… (More)

- Pawel Parys
- STACS
- 2011

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)

- Pawel Parys
- STACS
- 2012

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)

We consider the logic mso+u, which is monadic second-order logic extended with the unbounding quantifier. The unbounding quantifier is used to say that a property of finite sets holds for sets of arbitrarily large size. We prove that the logic is undecidable on infinite words, i.e. the mso+u theory of (N, ≤) is undecidable. This settles an open problem… (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)