326 research outputs found
Groups, Graphs, Languages, Automata, Games and Second-order Monadic Logic
In this paper we survey some surprising connections between group theory, the
theory of automata and formal languages, the theory of ends, infinite games of
perfect information, and monadic second-order logic
07441 Abstracts Collection -- Algorithmic-Logical Theory of Infinite Structures
From 28.10. to 02.11.2007, the Dagstuhl Seminar 07441 ``Algorithmic-Logical Theory of Infinite Structures\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
On factorisation forests
The theorem of factorisation forests shows the existence of nested
factorisations -- a la Ramsey -- for finite words. This theorem has important
applications in semigroup theory, and beyond. The purpose of this paper is to
illustrate the importance of this approach in the context of automata over
infinite words and trees. We extend the theorem of factorisation forest in two
directions: we show that it is still valid for any word indexed by a linear
ordering; and we show that it admits a deterministic variant for words indexed
by well-orderings. A byproduct of this work is also an improvement on the known
bounds for the original result. We apply the first variant for giving a
simplified proof of the closure under complementation of rational sets of words
indexed by countable scattered linear orderings. We apply the second variant in
the analysis of monadic second-order logic over trees, yielding new results on
monadic interpretations over trees. Consequences of it are new caracterisations
of prefix-recognizable structures and of the Caucal hierarchy.Comment: 27 page
Logics for Unranked Trees: An Overview
Labeled unranked trees are used as a model of XML documents, and logical
languages for them have been studied actively over the past several years. Such
logics have different purposes: some are better suited for extracting data,
some for expressing navigational properties, and some make it easy to relate
complex properties of trees to the existence of tree automata for those
properties. Furthermore, logics differ significantly in their model-checking
properties, their automata models, and their behavior on ordered and unordered
trees. In this paper we present a survey of logics for unranked trees
Logic and Automata
Mathematical logic and automata theory are two scientific disciplines with a fundamentally close relationship. The authors of Logic and Automata take the occasion of the sixtieth birthday of Wolfgang Thomas to present a tour d'horizon of automata theory and logic. The twenty papers in this volume cover many different facets of logic and automata theory, emphasizing the connections to other disciplines such as games, algorithms, and semigroup theory, as well as discussing current challenges in the field
The Cayley-graph of the queue monoid: logic and decidability
We investigate the decidability of logical aspects of graphs that arise as Cayley-graphs of the so-called queue monoids. These monoids model the behavior of the classical (reliable) fifo-queues. We answer a question raised by Huschenbett, Kuske, and Zetzsche and prove the decidability of the first-order theory of these graphs with the help of an - at least for the authors - new combination of the well-known method from Ferrante and Rackoff and an automata-based approach. On the other hand, we prove that the monadic second-order of the queue monoid's Cayley-graph is undecidable
Temporalized logics and automata for time granularity
Suitable extensions of the monadic second-order theory of k successors have
been proposed in the literature to capture the notion of time granularity. In
this paper, we provide the monadic second-order theories of downward unbounded
layered structures, which are infinitely refinable structures consisting of a
coarsest domain and an infinite number of finer and finer domains, and of
upward unbounded layered structures, which consist of a finest domain and an
infinite number of coarser and coarser domains, with expressively complete and
elementarily decidable temporal logic counterparts.
We obtain such a result in two steps. First, we define a new class of
combined automata, called temporalized automata, which can be proved to be the
automata-theoretic counterpart of temporalized logics, and show that relevant
properties, such as closure under Boolean operations, decidability, and
expressive equivalence with respect to temporal logics, transfer from component
automata to temporalized ones. Then, we exploit the correspondence between
temporalized logics and automata to reduce the task of finding the temporal
logic counterparts of the given theories of time granularity to the easier one
of finding temporalized automata counterparts of them.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym:
TPLP Category: Paper for Special Issue (Verification and Computational Logic)
Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September
200
Decidability Results for the Boundedness Problem
We prove decidability of the boundedness problem for monadic least
fixed-point recursion based on positive monadic second-order (MSO) formulae
over trees. Given an MSO-formula phi(X,x) that is positive in X, it is
decidable whether the fixed-point recursion based on phi is spurious over the
class of all trees in the sense that there is some uniform finite bound for the
number of iterations phi takes to reach its least fixed point, uniformly across
all trees. We also identify the exact complexity of this problem. The proof
uses automata-theoretic techniques. This key result extends, by means of
model-theoretic interpretations, to show decidability of the boundedness
problem for MSO and guarded second-order logic (GSO) over the classes of
structures of fixed finite tree-width. Further model-theoretic transfer
arguments allow us to derive major known decidability results for boundedness
for fragments of first-order logic as well as new ones
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