12,784 research outputs found
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
Learning-Based Synthesis of Safety Controllers
We propose a machine learning framework to synthesize reactive controllers
for systems whose interactions with their adversarial environment are modeled
by infinite-duration, two-player games over (potentially) infinite graphs. Our
framework targets safety games with infinitely many vertices, but it is also
applicable to safety games over finite graphs whose size is too prohibitive for
conventional synthesis techniques. The learning takes place in a feedback loop
between a teacher component, which can reason symbolically about the safety
game, and a learning algorithm, which successively learns an overapproximation
of the winning region from various kinds of examples provided by the teacher.
We develop a novel decision tree learning algorithm for this setting and show
that our algorithm is guaranteed to converge to a reactive safety controller if
a suitable overapproximation of the winning region can be expressed as a
decision tree. Finally, we empirically compare the performance of a prototype
implementation to existing approaches, which are based on constraint solving
and automata learning, respectively
What is a quantum computer, and how do we build one?
The DiVincenzo criteria for implementing a quantum computer have been seminal
in focussing both experimental and theoretical research in quantum information
processing. These criteria were formulated specifically for the circuit model
of quantum computing. However, several new models for quantum computing
(paradigms) have been proposed that do not seem to fit the criteria well. The
question is therefore what are the general criteria for implementing quantum
computers. To this end, a formal operational definition of a quantum computer
is introduced. It is then shown that according to this definition a device is a
quantum computer if it obeys the following four criteria: Any quantum computer
must (1) have a quantum memory; (2) facilitate a controlled quantum evolution
of the quantum memory; (3) include a method for cooling the quantum memory; and
(4) provide a readout mechanism for subsets of the quantum memory. The criteria
are met when the device is scalable and operates fault-tolerantly. We discuss
various existing quantum computing paradigms, and how they fit within this
framework. Finally, we lay out a roadmap for selecting an avenue towards
building a quantum computer. This is summarized in a decision tree intended to
help experimentalists determine the most natural paradigm given a particular
physical implementation
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Using formal methods to support testing
Formal methods and testing are two important approaches that assist in the development of high quality software. While traditionally these approaches have been seen as rivals, in recent
years a new consensus has developed in which they are seen as complementary. This article reviews the state of the art regarding ways in which the presence of a formal specification can be used to assist testing
Optimised determinisation and completion of finite tree automata
Determinisation and completion of finite tree automata are important
operations with applications in program analysis and verification. However, the
complexity of the classical procedures for determinisation and completion is
high. They are not practical procedures for manipulating tree automata beyond
very small ones. In this paper we develop an algorithm for determinisation and
completion of finite tree automata, whose worst-case complexity remains
unchanged, but which performs far better than existing algorithms in practice.
The critical aspect of the algorithm is that the transitions of the
determinised (and possibly completed) automaton are generated in a potentially
very compact form called product form, which can reduce the size of the
representation dramatically. Furthermore, the representation can often be used
directly when manipulating the determinised automaton. The paper contains an
experimental evaluation of the algorithm on a large set of tree automata
examples
A Case Study on Formal Verification of Self-Adaptive Behaviors in a Decentralized System
Self-adaptation is a promising approach to manage the complexity of modern
software systems. A self-adaptive system is able to adapt autonomously to
internal dynamics and changing conditions in the environment to achieve
particular quality goals. Our particular interest is in decentralized
self-adaptive systems, in which central control of adaptation is not an option.
One important challenge in self-adaptive systems, in particular those with
decentralized control of adaptation, is to provide guarantees about the
intended runtime qualities. In this paper, we present a case study in which we
use model checking to verify behavioral properties of a decentralized
self-adaptive system. Concretely, we contribute with a formalized architecture
model of a decentralized traffic monitoring system and prove a number of
self-adaptation properties for flexibility and robustness. To model the main
processes in the system we use timed automata, and for the specification of the
required properties we use timed computation tree logic. We use the Uppaal tool
to specify the system and verify the flexibility and robustness properties.Comment: In Proceedings FOCLASA 2012, arXiv:1208.432
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