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TreeWalking Pebble Automata
 Jewels are forever, contributions to Theoretical Computer Science in honor of Arto Salomaa
, 1999
"... this paper is to investigate the power of treewalking automata with pebbles. Obviously, the unrestricted use of pebbles leads to a class of tree languages much larger than the regular tree languages, in fact to all tree languages in NSPACE(logn). Thus, we restrict the automaton to the recursive use ..."
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Cited by 38 (2 self)
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this paper is to investigate the power of treewalking automata with pebbles. Obviously, the unrestricted use of pebbles leads to a class of tree languages much larger than the regular tree languages, in fact to all tree languages in NSPACE(logn). Thus, we restrict the automaton to the recursive use of pebbles, in the sense that the life times of pebbles, i.e., the times between dropping a pebble and lifting it again, are properly nested. A similar, but stronger, nesting requirement is studied in [13] for 2way automata on strings. We prove in Section 5 that our restriction indeed guarantees that all tree languages recognized by the treewalking pebble automaton are regular, but we conjecture that the automaton is not powerful enough to recognize all regular tree languages. In Section 6 we generalize the notion of pebble to that of a \setpebble", in such a way that the treewalking setpebble automaton recognizes exactly the regular tree languages.
Tree Automata for Code Selection
, 1994
"... We deal with the generation of code selectors in compiler backends. The fundamental concepts are systematically derived from the theory of regular tree grammars and finite tree automata. We use this general approach to construct algorithms that generalize and improve existing methods. 1 Introduction ..."
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Cited by 28 (0 self)
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We deal with the generation of code selectors in compiler backends. The fundamental concepts are systematically derived from the theory of regular tree grammars and finite tree automata. We use this general approach to construct algorithms that generalize and improve existing methods. 1 Introduction A code generator for a compiler is applied to an intermediate representation (IR) of the input program that has been computed during preceding phases of compilation. This intermediate representation can be viewed as code for an abstract machine. The task of code generation is to translate this code into an efficient sequence of instructions for a concrete machine. Besides register allocation and instruction scheduling (for processors with pipelined architectures), code selection, i.e., the selection of instructions, is one subtask of code generation. It is especially important for CISC (Complex I nstruction Set Computer) architectures where there are usually many possibilities to generat...
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 ..."
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Cited by 25 (8 self)
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. 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...
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 a regular ..."
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Cited by 6 (0 self)
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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.
Making finitestate methods applicable to languages beyond contextfreeness via multidimensional trees
, 2008
"... Abstract. We provide a new termlike representation for multidimensional trees as defined by Rogers [8,9] which establishes them as a direct generalization of classical trees. As a consequence these structures can be used as input for finitestate applications based on classical tree language theor ..."
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Cited by 2 (2 self)
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Abstract. We provide a new termlike representation for multidimensional trees as defined by Rogers [8,9] which establishes them as a direct generalization of classical trees. As a consequence these structures can be used as input for finitestate applications based on classical tree language theory. Via the correspondence between string and tree languages these applications can then be conceived to be able to process even some language classes beyond contextfreeness.
Ambiguity, Valuedness and Costs
, 1992
"... This survey reports results on the ambiguity of finite tree automata, the valuedness of bottomup finite state tree transducers and boundedness of cost automata. ..."
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Cited by 2 (0 self)
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This survey reports results on the ambiguity of finite tree automata, the valuedness of bottomup finite state tree transducers and boundedness of cost automata.
The Delta Operation: From Strings to Trees to Strings
, 2002
"... The delta of a language L consists of the yields of trees of which all paths are in L. The contextfree languages are the deltas of the regular languages. The indexed languages are the deltas of the deterministic contextfree languages. In general, the nondeterministic (n+1)iterated pushdown la ..."
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The delta of a language L consists of the yields of trees of which all paths are in L. The contextfree languages are the deltas of the regular languages. The indexed languages are the deltas of the deterministic contextfree languages. In general, the nondeterministic (n+1)iterated pushdown languages are the deltas of the deterministic n iterated pushdown languages. The recursively enumerable languages are the deltas of the contextfree languages. The delta of a string relation R consists of the yields of trees of which all paths are in the Rimage of one string. The ET0L languages are the deltas of the relations recognized by deterministic twotape finite automata. The recursively enumerable languages are the deltas of the finite state transductions.
A Note on Trees, Tables and Algorithms
"... Several algorithms for optimal vertex subsets in trees are given by simple tables. In this paper we investigate the properties of and operations on these tables. We use known techniques for combining tables to correct a table in the literature; give a necessary and sufficient condition for a table t ..."
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Several algorithms for optimal vertex subsets in trees are given by simple tables. In this paper we investigate the properties of and operations on these tables. We use known techniques for combining tables to correct a table in the literature; give a necessary and sufficient condition for a table to correspond to some tree property; discuss the question of dividing one table by another; explain how to derive a table from a set of representatives; and apply this to finding the table for the parameter external redundance. All of this is facilitated by computer software.