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14
Treewalking automata
"... A survey of treewalking automata. The main focus is on how the expressive power is changed by adding features such as pebbles or nondeterminism. ..."
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A survey of treewalking automata. The main focus is on how the expressive power is changed by adding features such as pebbles or nondeterminism.
Nested pebbles and transitive closure, in
 Proceedings 23rd Annual Symposium on Theoretical Aspects of Computer Science, STACS 2006
, 2006
"... Abstract. Firstorder logic with kary deterministic transitive closure has the same power as twoway khead deterministic automata that use a finite set of nested pebbles. This result is valid for strings, ranked trees, and in general for families of graphs having a fixed automaton that can be use ..."
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Abstract. Firstorder logic with kary deterministic transitive closure has the same power as twoway khead deterministic automata that use a finite set of nested pebbles. This result is valid for strings, ranked trees, and in general for families of graphs having a fixed automaton that can be used to traverse the nodes of each of the graphs in the family. Other examples of such families are grids, toruses, and rectangular mazes.
Complementing deterministic treewalking automata
 Inform. Process. Lett
"... We consider various kinds of deterministic treewalking automata, with and without pebbles, over ranked and unranked trees. For each such kind of automata we show that there is an equivalent one which never loops. The main consequence of this result is the closure under complementation of the vari ..."
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We consider various kinds of deterministic treewalking automata, with and without pebbles, over ranked and unranked trees. For each such kind of automata we show that there is an equivalent one which never loops. The main consequence of this result is the closure under complementation of the various types of automata we consider with a focus on the number of pebbles used in order to complement the automata. 1
Weighted TreeWalking Automata
 ACTA CYBERNETICA 19 (2009) 275–293
, 2009
"... We define weighted treewalking automata. We show that the class of tree series recognizable by weighted treewalking automata over a commutative semiring K is a subclass of the class of regular tree series over K. If K is not a ring, then the inclusion is strict. ..."
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We define weighted treewalking automata. We show that the class of tree series recognizable by weighted treewalking automata over a commutative semiring K is a subclass of the class of regular tree series over K. If K is not a ring, then the inclusion is strict.
Walking automata in the free inverse monoid
, 2013
"... In this paper, we study languages of birooted trees or, following ScheiblichMunn’s theorem, subsets of free inverse monoids. Extending the classical notion of rational languages with a projection operatorthat maps every set of birooted trees to the subset of its idempotent elements it is first ..."
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In this paper, we study languages of birooted trees or, following ScheiblichMunn’s theorem, subsets of free inverse monoids. Extending the classical notion of rational languages with a projection operatorthat maps every set of birooted trees to the subset of its idempotent elements it is first shown that the hierarchy induced by the nesting depth of that projection operator simply correspond the hierarchy induced by the number of (invisible) pebbles used in tree walking automata extended to birooted trees (with complete run semantics). Then, analyzing further the behavior of these walking automata by allowing partial accepting runs runs that are no longer required to traverse the complete input structure it is also shown that finite boolean combinations of languages recognizable by finite state walking automata (with partial run semantics) are equivalent to languages recognizable by means of (some computable notion of) premorphisms from free inverse monoids into finite partially ordered monoids. The various classes of definable languages that are considered in this paper are compared with the class of languages definable in Monadic Second Order (MSO) logic: a typical yardstick of expressive power.
Foundations of XML based on Logic and Automata: a snapshot
"... XML query and schema languages have some obvious connections ..."
Weighted Expressions and DFS Tree Automata
, 2011
"... We introduce weighted expressions, a calculus to express quantitative properties over unranked trees. They involve products and sums from a semiring as well as classical boolean formulas. We show that weighted expressions are expressively equivalent to a new class of weighted treewalking automata. ..."
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We introduce weighted expressions, a calculus to express quantitative properties over unranked trees. They involve products and sums from a semiring as well as classical boolean formulas. We show that weighted expressions are expressively equivalent to a new class of weighted treewalking automata. This new automata model is equipped with pebbles, and follows a depthfirstsearch policy in the tree.