199,572 research outputs found
Regular sets over extended tree structures
We investigate notions of decidability and definability for the Monadic Second-Order Logic of labeled tree structures, and links with finite automata using oracles to test input prefixes. A general framework is defined allowing to transfer some MSO-properties from a graph-structure to a labeled tree structure. Transferred properties are decidability of sentences and existence of a definable model for every satisfiable formula. A class of finite automata with prefix-oracles is also defined, recognizing exactly languages defined by MSO-formulas in any labeled tree-structure. Applying these results, the well-known equality between languages recognized by finite automata,sets of vertices MSO definable in a tree-structure and sets of pushdown contexts generated by pushdown-automata is extended to iterated pushdown automata
Transforming structures by set interpretations
We consider a new kind of interpretation over relational structures: finite
sets interpretations. Those interpretations are defined by weak monadic
second-order (WMSO) formulas with free set variables. They transform a given
structure into a structure with a domain consisting of finite sets of elements
of the orignal structure. The definition of these interpretations directly
implies that they send structures with a decidable WMSO theory to structures
with a decidable first-order theory. In this paper, we investigate the
expressive power of such interpretations applied to infinite deterministic
trees. The results can be used in the study of automatic and tree-automatic
structures.Comment: 36 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
Observation and Distinction. Representing Information in Infinite Games
We compare two approaches for modelling imperfect information in infinite games by using finite-state automata. The first, more standard approach views information as the result of an observation process driven by a sequential Mealy machine. In contrast, the second approach features indistinguishability relations described by synchronous two-tape automata.
The indistinguishability-relation model turns out to be strictly more expressive than the one based on observations. We present a characterisation of the indistinguishability relations that admit a representation as a finite-state observation function. We show that the characterisation is decidable, and give a procedure to construct a corresponding Mealy machine whenever one exists
Advances and applications of automata on words and trees : abstracts collection
From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 "Advances and Applications of Automata on Words and Trees" was held in Schloss Dagstuhl - Leibniz Center for Informatics. 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
Reachability analysis of first-order definable pushdown systems
We study pushdown systems where control states, stack alphabet, and
transition relation, instead of being finite, are first-order definable in a
fixed countably-infinite structure. We show that the reachability analysis can
be addressed with the well-known saturation technique for the wide class of
oligomorphic structures. Moreover, for the more restrictive homogeneous
structures, we are able to give concrete complexity upper bounds. We show ample
applicability of our technique by presenting several concrete examples of
homogeneous structures, subsuming, with optimal complexity, known results from
the literature. We show that infinitely many such examples of homogeneous
structures can be obtained with the classical wreath product construction.Comment: to appear in CSL'1
Isomorphisms of scattered automatic linear orders
We prove that the isomorphism of scattered tree automatic linear orders as
well as the existence of automorphisms of scattered word automatic linear
orders are undecidable. For the existence of automatic automorphisms of word
automatic linear orders, we determine the exact level of undecidability in the
arithmetical hierarchy
The Isomorphism Relation Between Tree-Automatic Structures
An -tree-automatic structure is a relational structure whose domain
and relations are accepted by Muller or Rabin tree automata. We investigate in
this paper the isomorphism problem for -tree-automatic structures. We
prove first that the isomorphism relation for -tree-automatic boolean
algebras (respectively, partial orders, rings, commutative rings, non
commutative rings, non commutative groups, nilpotent groups of class n >1) is
not determined by the axiomatic system ZFC. Then we prove that the isomorphism
problem for -tree-automatic boolean algebras (respectively, partial
orders, rings, commutative rings, non commutative rings, non commutative
groups, nilpotent groups of class n >1) is neither a -set nor a
-set
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