8,675 research outputs found
Architectures in parametric component-based systems: Qualitative and quantitative modelling
One of the key aspects in component-based design is specifying the software
architecture that characterizes the topology and the permissible interactions
of the components of a system. To achieve well-founded design there is need to
address both the qualitative and non-functional aspects of architectures. In
this paper we study the qualitative and quantitative formal modelling of
architectures applied on parametric component-based systems, that consist of an
unknown number of instances of each component. Specifically, we introduce an
extended propositional interaction logic and investigate its first-order level
which serves as a formal language for the interactions of parametric systems.
Our logics achieve to encode the execution order of interactions, which is a
main feature in several important architectures, as well as to model recursive
interactions. Moreover, we prove the decidability of equivalence,
satisfiability, and validity of first-order extended interaction logic
formulas, and provide several examples of formulas describing well-known
architectures. We show the robustness of our theory by effectively extending
our results for parametric weighted architectures. For this, we study the
weighted counterparts of our logics over a commutative semiring, and we apply
them for modelling the quantitative aspects of concrete architectures. Finally,
we prove that the equivalence problem of weighted first-order extended
interaction logic formulas is decidable in a large class of semirings, namely
the class (of subsemirings) of skew fields.Comment: 53 pages, 11 figure
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
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
First-order definable string transformations
The connection between languages defined by computational models and logic
for languages is well-studied. Monadic second-order logic and finite automata
are shown to closely correspond to each-other for the languages of strings,
trees, and partial-orders. Similar connections are shown for first-order logic
and finite automata with certain aperiodicity restriction. Courcelle in 1994
proposed a way to use logic to define functions over structures where the
output structure is defined using logical formulas interpreted over the input
structure. Engelfriet and Hoogeboom discovered the corresponding "automata
connection" by showing that two-way generalised sequential machines capture the
class of monadic-second order definable transformations. Alur and Cerny further
refined the result by proposing a one-way deterministic transducer model with
string variables---called the streaming string transducers---to capture the
same class of transformations. In this paper we establish a transducer-logic
correspondence for Courcelle's first-order definable string transformations. We
propose a new notion of transition monoid for streaming string transducers that
involves structural properties of both underlying input automata and variable
dependencies. By putting an aperiodicity restriction on the transition monoids,
we define a class of streaming string transducers that captures exactly the
class of first-order definable transformations.Comment: 31 page
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
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