Mikolaj Bojanczyk

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Motivated by reasoning tasks for XML languages, the satisfiability problem of logics on <i>data trees</i> is investigated. The nodes of a data tree have a <i>label</i> from a finite set and a <i>data value</i> from a possibly infinite set. It is shown that satisfiability for two-variable first-order logic is decidable if the tree structure can be accessed(More)
In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been already considered in the realm of semistructured data, timed automata and extended temporal logics. It is shown that satisfiability for the two-variable first-order logic FO<sup>2</sup>(~,&lt;,+1) is decidable over finite(More)
In a <i>data word</i> each position carries a label from a finite alphabet and a data value from some infinite domain. This model has been already considered in the realm of semistructured data, timed automata, and extended temporal logics. This article shows that satisfiability for the two-variable fragment FO<sup>2</sup>(&sim;,&lt;,+1) of first-order(More)
Tree-walking automata are a natural sequential model for recognizing tree languages. Every tree language recognized by a tree-walking automaton is regular. In this paper, we present a tree language which is regular but not recognized by any (nondeterministic) tree-walking automaton. This settles a conjecture of Engelfriet, Hoogeboom and Van Best. Moreover,(More)
Two variants of pebble tree-walking automata on trees are considered that were introduced in the literature. It is shown that for each number of pebbles, the two models have the same expressive power both in the deterministic case and in the nondeterministic case. Furthermore, nondeterministic (resp. deterministic) treewalking automata with n+ 1 pebbles can(More)
A new class of languages of infinite words is introduced, called the max-regular languages, extending the class of ω-regular languages. The class has two equivalent descriptions: in terms of automata (a type of deterministic counter automaton), and in terms of logic (weak monadic second-order logic with a bounding quantifier). Effective translations between(More)
We describe the expressive power of temporal branching time logics that use the modalities EX and EF. We give a forbidden pattern characterization of the tree languages definable in three logics: EX, EF and EX+EF. The properties in these characterizations can be verified in polynomial time when given a minimal deterministic bottom-up tree automaton. We(More)
If in a transformation semigroup we assume that the set being acted upon has a semigroup structure, then the transformation semigroup can be used to recognize languages of unranked trees. This observation allows us to examine the relationship connecting languages of unranked trees with standard algebraic concepts such as aperiodicity, idempotency,(More)
The paper explores the relationship between tree languages definable in LTL, CTL, and ACTL, the fragment of CTL where only universal path quantification is allowed. The common fragment of LTL and ACTL is shown to be strictly smaller than the common fragment of LTL and CTL. Furthermore, an algorithm is presented for deciding if an LTL formula can be(More)