Results 1 
3 of
3
A Comparison of Tree Transductions defined by Monadic Second Order Logic and by Attribute Grammars
, 1998
"... . Two wellknown formalisms for the specication and computation of tree transductions are compared: the mso graph transducer and the attributed tree transducer with lookahead, respectively. The mso graph transducer, restricted to trees, uses monadic second order logic to dene the output tree in ..."
Abstract

Cited by 32 (8 self)
 Add to MetaCart
(Show Context)
. Two wellknown formalisms for the specication and computation of tree transductions are compared: the mso graph transducer and the attributed tree transducer with lookahead, respectively. The mso graph transducer, restricted to trees, uses monadic second order logic to dene the output tree in terms of the input tree. The attributed tree transducer is an attribute grammar in which all attributes are trees; it is preceded by a lookahead phase in which all attributes have nitely many values. The main result is that these formalisms are equivalent, i.e., that the attributed tree transducer with lookahead is an appropriate implementation model for the tree transductions that are speciable in mso logic. This result holds for mso graph transducers that produce trees with shared subtrees. If no sharing is allowed, the attributed tree transducer satises the single use restriction. 1 Introduction Formulas of monadic second order (mso) logic can be used to express properti...
Characterization of Properties and Relations defined in Monadic Second Order Logic on the Nodes of Trees
, 1997
"... . A formula from monadic second order (mso) logic with one free variable can be used to define a property of the nodes of a tree. Similarly, an mso formula with two free variables can be used to define a binary relation between the nodes of a tree. It is proved that a node relation is mso definable ..."
Abstract

Cited by 15 (1 self)
 Add to MetaCart
(Show Context)
. A formula from monadic second order (mso) logic with one free variable can be used to define a property of the nodes of a tree. Similarly, an mso formula with two free variables can be used to define a binary relation between the nodes of a tree. It is proved that a node relation is mso definable iff it can be computed by a finitestate treewalking automaton, provided the automaton can test mso definable properties of the nodes of the tree; if the relation is a function, the automaton is deterministic. It is also proved that a node property is mso definable iff it can be computed by an attribute grammar of which all attributes have finitely many values. mso definable node properties are computable in linear time, mso definable node relations in quadratic time, and mso definable node functions in linear time. 1 Introduction It is shown in [Buc, Elg] that a set of strings can be defined in monadic second order logic if and only if it can be recognized by a finitestate automaton. Th...
Trips on Trees
 ACTA CYBERNETICA
, 1999
"... A "trip" is a triple (g; u; v) where g is, in general, a graph and u and v are nodes of that graph. The trip is from u to v on the graph g. For the special case that g is a tree (or even a string) we investigate ways of specifying and implementing sets of trips. The main result is that ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
A "trip" is a triple (g; u; v) where g is, in general, a graph and u and v are nodes of that graph. The trip is from u to v on the graph g. For the special case that g is a tree (or even a string) we investigate ways of specifying and implementing sets of trips. The main result is that a regular set of trips, specified as a regular tree language, can be implemented by a treewalking automaton that uses marbles and one pebble.