323 research outputs found
In the Maze of Data Languages
In data languages the positions of strings and trees carry a label from a
finite alphabet and a data value from an infinite alphabet. Extensions of
automata and logics over finite alphabets have been defined to recognize data
languages, both in the string and tree cases. In this paper we describe and
compare the complexity and expressiveness of such models to understand which
ones are better candidates as regular models
An Application of the Feferman-Vaught Theorem to Automata and Logics for<br> Words over an Infinite Alphabet
We show that a special case of the Feferman-Vaught composition theorem gives
rise to a natural notion of automata for finite words over an infinite
alphabet, with good closure and decidability properties, as well as several
logical characterizations. We also consider a slight extension of the
Feferman-Vaught formalism which allows to express more relations between
component values (such as equality), and prove related decidability results.
From this result we get new classes of decidable logics for words over an
infinite alphabet.Comment: 24 page
Monadic Second-Order Logic with Arbitrary Monadic Predicates
We study Monadic Second-Order Logic (MSO) over finite words, extended with
(non-uniform arbitrary) monadic predicates. We show that it defines a class of
languages that has algebraic, automata-theoretic and machine-independent
characterizations. We consider the regularity question: given a language in
this class, when is it regular? To answer this, we show a substitution property
and the existence of a syntactical predicate.
We give three applications. The first two are to give very simple proofs that
the Straubing Conjecture holds for all fragments of MSO with monadic
predicates, and that the Crane Beach Conjecture holds for MSO with monadic
predicates. The third is to show that it is decidable whether a language
defined by an MSO formula with morphic predicates is regular.Comment: Conference version: MFCS'14, Mathematical Foundations of Computer
Science Journal version: ToCL'17, Transactions on Computational Logi
An expressive completeness theorem for coalgebraic modal mu-calculi
Generalizing standard monadic second-order logic for Kripke models, we
introduce monadic second-order logic interpreted over coalgebras for an
arbitrary set functor. We then consider invariance under behavioral equivalence
of MSO-formulas. More specifically, we investigate whether the coalgebraic
mu-calculus is the bisimulation-invariant fragment of the monadic second-order
language for a given functor. Using automatatheoretic techniques and building
on recent results by the third author, we show that in order to provide such a
characterization result it suffices to find what we call an adequate uniform
construction for the coalgebraic type functor. As direct applications of this
result we obtain a partly new proof of the Janin-Walukiewicz Theorem for the
modal mu-calculus, avoiding the use of syntactic normal forms, and bisimulation
invariance results for the bag functor (graded modal logic) and all exponential
polynomial functors (including the "game functor"). As a more involved
application, involving additional non-trivial ideas, we also derive a
characterization theorem for the monotone modal mu-calculus, with respect to a
natural monadic second-order language for monotone neighborhood models.Comment: arXiv admin note: substantial text overlap with arXiv:1501.0721
Weak MSO+U with Path Quantifiers over Infinite Trees
This paper shows that over infinite trees, satisfiability is decidable for
weak monadic second-order logic extended by the unbounding quantifier U and
quantification over infinite paths. The proof is by reduction to emptiness for
a certain automaton model, while emptiness for the automaton model is decided
using profinite trees.Comment: version of an ICALP 2014 paper with appendice
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
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
Infinite and Bi-infinite Words with Decidable Monadic Theories
We study word structures of the form where is either
or , is the natural linear ordering on and
is a predicate on . In particular we show:
(a) The set of recursive -words with decidable monadic second order
theories is -complete.
(b) Known characterisations of the -words with decidable monadic
second order theories are transfered to the corresponding question for
bi-infinite words.
(c) We show that such "tame" predicates exist in every Turing degree.
(d) We determine, for , the number of predicates
such that and
are indistinguishable.
Through these results we demonstrate similarities and differences between
logical properties of infinite and bi-infinite words
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