3,171 research outputs found
Two-Way Unary Temporal Logic over Trees
We consider a temporal logic EF+F^-1 for unranked, unordered finite trees.
The logic has two operators: EF\phi, which says "in some proper descendant \phi
holds", and F^-1\phi, which says "in some proper ancestor \phi holds". We
present an algorithm for deciding if a regular language of unranked finite
trees can be expressed in EF+F^-1. The algorithm uses a characterization
expressed in terms of forest algebras.Comment: 29 pages. Journal version of a LICS 07 pape
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
First-Order and Temporal Logics for Nested Words
Nested words are a structured model of execution paths in procedural
programs, reflecting their call and return nesting structure. Finite nested
words also capture the structure of parse trees and other tree-structured data,
such as XML. We provide new temporal logics for finite and infinite nested
words, which are natural extensions of LTL, and prove that these logics are
first-order expressively-complete. One of them is based on adding a "within"
modality, evaluating a formula on a subword, to a logic CaRet previously
studied in the context of verifying properties of recursive state machines
(RSMs). The other logic, NWTL, is based on the notion of a summary path that
uses both the linear and nesting structures. For NWTL we show that
satisfiability is EXPTIME-complete, and that model-checking can be done in time
polynomial in the size of the RSM model and exponential in the size of the NWTL
formula (and is also EXPTIME-complete). Finally, we prove that first-order
logic over nested words has the three-variable property, and we present a
temporal logic for nested words which is complete for the two-variable fragment
of first-order.Comment: revised and corrected version of Mar 03, 201
Reasoning about XML with temporal logics and automata
We show that problems arising in static analysis of XML specifications and transformations can be dealt with using techniques similar to those developed for static analysis of programs. Many properties of interest in the XML context are related to navigation, and can be formulated in temporal logics for trees. We choose a logic that admits a simple single-exponential translation into unranked tree automata, in the spirit of the classical LTL-to-Büchi automata translation. Automata arising from this translation have a number of additional properties; in particular, they are convenient for reasoning about unary node-selecting queries, which are important in the XML context. We give two applications of such reasoning: one deals with a classical XML problem of reasoning about navigation in the presence of schemas, and the other relates to verifying security properties of XML views
Monadic second order finite satisfiability and unbounded tree-width
The finite satisfiability problem of monadic second order logic is decidable
only on classes of structures of bounded tree-width by the classic result of
Seese (1991). We prove the following problem is decidable:
Input: (i) A monadic second order logic sentence , and (ii) a
sentence in the two-variable fragment of first order logic extended
with counting quantifiers. The vocabularies of and may
intersect.
Output: Is there a finite structure which satisfies such
that the restriction of the structure to the vocabulary of has bounded
tree-width? (The tree-width of the desired structure is not bounded.)
As a consequence, we prove the decidability of the satisfiability problem by
a finite structure of bounded tree-width of a logic extending monadic second
order logic with linear cardinality constraints of the form
, where the and
are monadic second order variables. We prove the decidability of a similar
extension of WS1S
On relating CTL to Datalog
CTL is the dominant temporal specification language in practice mainly due to
the fact that it admits model checking in linear time. Logic programming and
the database query language Datalog are often used as an implementation
platform for logic languages. In this paper we present the exact relation
between CTL and Datalog and moreover we build on this relation and known
efficient algorithms for CTL to obtain efficient algorithms for fragments of
stratified Datalog. The contributions of this paper are: a) We embed CTL into
STD which is a proper fragment of stratified Datalog. Moreover we show that STD
expresses exactly CTL -- we prove that by embedding STD into CTL. Both
embeddings are linear. b) CTL can also be embedded to fragments of Datalog
without negation. We define a fragment of Datalog with the successor build-in
predicate that we call TDS and we embed CTL into TDS in linear time. We build
on the above relations to answer open problems of stratified Datalog. We prove
that query evaluation is linear and that containment and satisfiability
problems are both decidable. The results presented in this paper are the first
for fragments of stratified Datalog that are more general than those containing
only unary EDBs.Comment: 34 pages, 1 figure (file .eps
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