Optimal control and geodesic flows

In this paper we analyze and generalize, from the point of view of the maximum principle, a class of nonlinear optimal control problems originally introduced in Brockett (1994). The optimal control problems discussed here lie on the adjoint orbits of compact Lie groups or on Grassmann manifolds and the structure of the equations that arise depends on the metric used - the so-called normal metric. We consider some special cases of the general problem and their meaning from the point of view of Riemannian geometry and Hamiltonian mechanics.     

Condensed state spaces for symmetrical Coloured Petri Nets

This paper deals with state spaces. A state space is a directed graph with a node for each reachable state and an arc for each possible state change. We describe how symmetries of the modelled system can be exploited to obtain much more succinct state space analysis. The symmetries induce equivalence classes of states and equivalence classes of state changes. It is then possible to construct a condensed state space where each node represents an equivalence class of states while each arc represents an equivalence class of state changes. Such a condensed state space is often much smaller than the full state space and it is also much faster to construct. Nevertheless, it is possible to use the condensed state space to verify the same kind of behavioural properties as the full state space. hence, we do not lose analytic power.We define state spaces and condensed state spaces for a language called Coloured Petri Nets (CP-nets). This language is in widespread use for the modelling and analysis of concurrent systems. However, our techniques are general and they can be used for many other kinds of labelled transition systems. The paper does not assume that the reader is familiar with CP-nets (or Petri nets in general)—although such knowledge will, of course, be a help. The first four sections of the paper introduce the basic concepts of CP-nets. The next three sections deal with state spaces, condensed state spaces and computer tools for state space analysis. Finally, there is a short conclusion.     

ReSpecT Nets: Towards an Analysis Methodology for ReSpecT Specifications

A key feature for infrastructures providing coordination services is the ability to define the behaviour of coordination abstractions according to the requirements identified at design-time. We take as a representative for this scenario the logic-based language ReSpecT (Reaction Specification Tuples), used to program the reactive behaviour of tuple centres. ReSpecT specifications are at the core of the engineering methodology underlying the TuCSoN infrastructure, and are therefore the “conceptual place” where formal methods can be fruitfully applied to guarantee relevant system properties.In this paper we introduce ReSpecT nets, a formalism that can be used to describe reactive behaviours that can succeed and fail, and that allows for an encoding to Petri nets with inhibitor arcs. ReSpecT nets are introduced to give a core model to a fragment of the ReSpecT language, and to pave the way for devising an analysis methodology including formal verification of safety and liveness properties. In particular, we provide a semantics to ReSpecT specifications through a mapping to ReSpecT nets. The potential of this approach for the analysis of ReSpecT specifications is discussed, presenting initial results for the analysis of safety properties.     

Robustness of temporal logic specifications for continuous-time signals

In this paper, we consider the robust interpretation of Metric Temporal Logic (MTL) formulas over signals that take values in metric spaces. For such signals, which are generated by systems whose states are equipped with non-trivial metrics, for example continuous or hybrid, robustness is not only natural, but also a critical measure of system performance. Thus, we propose multi-valued semantics for MTL formulas, which capture not only the usual Boolean satisfiability of the formula, but also topological information regarding the distance, ε$\epsilon$, from unsatisfiability. We prove that any other signal that remains ε$\epsilon$-close to the initial one also satisfies the same MTL specification under the usual Boolean semantics. Finally, our framework is applied to the problem of testing formulas of two fragments of MTL, namely Metric Interval Temporal Logic (MITL) and closed Metric Temporal Logic (clMTL), over continuous-time signals using only discrete-time analysis. The motivating idea behind our approach is that if the continuous-time signal fulfills certain conditions and the discrete-time signal robustly satisfies the temporal logic specification, then the corresponding continuous-time signal should also satisfy the same temporal logic specification.     

Mobile Agents in Interaction Spaces

Mobile agent systems are difficult to reason about and implement efficiently and safely. Theoretical work, most notably process calculi, provide solid semantics for mobile systems. However, the theory is often too abstract to match with the requirements of practical implementations. To fill this gap, intermediate models must be proposed. We present in this paper such a model named Interaction Spaces, a metaphor of geometrical spaces in which agents interact through simple transformations. The framework captures high-level distributed semantics, most notably asynchronous, multicast communications on FIFO channels. It also refines and implements the channel passing feature of the pi-calculus, together with the mobility of agent themselves. Above interaction spaces, we propose a full-fledged agent calculus and its associated operational semantics.     

Some approaches to improve tree-based nearest neighbour search algorithms

Nearest neighbour search is a widely used technique in pattern recognition. During the last three decades a large number of fast algorithms have been proposed. In this work we are interested in algorithms that can be used with any dissimilarity function provided that it fits the mathematical notion of distance.Some of such algorithms organize, in preprocessing time, the data in a tree structure that is traversed in search time to find the nearest neighbour. The speedup is obtained using some pruning rules that avoid the traversal of some parts of the tree.In this work two new decomposition methods to build the tree and three new pruning rules are explored. The behaviour of our proposal is studied through experiments with synthetic and real data.     

一种基于串空间的不变集生成算法

在串空间模型中将理想定义为其不变集的代数结构,并利用它的性质描述攻击者攻击行为的能力界限,将安全协议的形式化分析规约为代数系统的不变集生成.引入hash:K×Bn-1→B,扩充了原模型中的子句关系,并给出理想诚实性判定定理在扩充子句关系下仍成立的结论.在此基础之上,提出诚实性判定条件的可满足性定理和一种新的不变集生成算法.     

非均匀采样曲线的支持向量机重建

简要介绍了回归支持向量机的理论，根据框架理论导出了非均匀采样曲线能够完全重建的条件，在此基础上分别利用框架迭代算法和回归支持向量机对平移不变空间中的同一非均匀采样曲线进行重建，重建结果表明若用回归支持向量机方法对平移不变空间中的非均匀采样曲线进行稳定重建则采样集须满足由框架理论导出的完全重建条件。     

Rudiments of rough sets

Worldwide, there has been a rapid growth in interest in rough set theory and its applications in recent years. Evidence of this can be found in the increasing number of high-quality articles on rough sets and related topics that have been published in a variety of international journals, symposia, workshops, and international conferences in recent years. In addition, many international workshops and conferences have included special sessions on the theory and applications of rough sets in their programs. Rough set theory has led to many interesting applications and extensions. It seems that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences, especially in research areas such as machine learning, intelligent systems, inductive reasoning, pattern recognition, mereology, knowledge discovery, decision analysis, and expert systems. In the article, we present the basic concepts of rough set theory and point out some rough set-based research directions and applications.