11,120 research outputs found
Algebraic recognizability of regular tree languages
We propose a new algebraic framework to discuss and classify recognizable
tree languages, and to characterize interesting classes of such languages. Our
algebraic tool, called preclones, encompasses the classical notion of syntactic
Sigma-algebra or minimal tree automaton, but adds new expressivity to it. The
main result in this paper is a variety theorem \`{a} la Eilenberg, but we also
discuss important examples of logically defined classes of recognizable tree
languages, whose characterization and decidability was established in recent
papers (by Benedikt and S\'{e}goufin, and by Bojanczyk and Walukiewicz) and can
be naturally formulated in terms of pseudovarieties of preclones. Finally, this
paper constitutes the foundation for another paper by the same authors, where
first-order definable tree languages receive an algebraic characterization
Tree transducers, L systems, and two-way machines
A relationship between parallel rewriting systems and two-way machines is investigated. Restrictions on the “copying power” of these devices endow them with rich structuring and give insight into the issues of determinism, parallelism, and copying. Among the parallel rewriting systems considered are the top-down tree transducer; the generalized syntax-directed translation scheme and the ETOL system, and among the two-way machines are the tree-walking automaton, the two-way finite-state transducer, and (generalizations of) the one-way checking stack automaton. The. relationship of these devices to macro grammars is also considered. An effort is made .to provide a systematic survey of a number of existing results
A B\"uchi-Elgot-Trakhtenbrot theorem for automata with MSO graph storage
We introduce MSO graph storage types, and call a storage type MSO-expressible
if it is isomorphic to some MSO graph storage type. An MSO graph storage type
has MSO-definable sets of graphs as storage configurations and as storage
transformations. We consider sequential automata with MSO graph storage and
associate with each such automaton a string language (in the usual way) and a
graph language; a graph is accepted by the automaton if it represents a correct
sequence of storage configurations for a given input string. For each MSO graph
storage type, we define an MSO logic which is a subset of the usual MSO logic
on graphs. We prove a B\"uchi-Elgot-Trakhtenbrot theorem, both for the string
case and the graph case. Moreover, we prove that (i) each MSO graph
transduction can be used as storage transformation in an MSO graph storage
type, (ii) every automatic storage type is MSO-expressible, and (iii) the
pushdown operator on storage types preserves the property of
MSO-expressibility. Thus, the iterated pushdown storage types are
MSO-expressible
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