A Modal Characterization of Alternating Approximate Bisimilarity

Recently, alternating transition systems are adopted to describe control systems with disturbances and their finite abstract systems. In order to capture the equivalence relation between these systems, a notion of alternating approximate bisimilarity is introduced. This paper aims to establish a modal characterization for alternating approximate bisimilarity. Moreover, based on this result, we provide a link between specifications satisfied by the samples of control systems with disturbances and their finite abstractions.Comment: 27 pages, 2 figure

Greatest solutions of equations in CLLR\text{CLL}_R and its application

This paper explores the process calculus $\text{CLL}_R$ furtherly. First, we prove that for any equation $X=_{RS} t_X$ such that $X$ is strongly guarded in $t_X$, $\langle X|X=t_X \rangle$ is the largest solution w.r.t $\sqsubseteq_{RS}$. Second, we encode a fragment of action-based CTL in $\text{CLL}_R$.Comment: 13 pages. arXiv admin note: text overlap with arXiv:1301.335

On the greatest solution of equations in CLLR\text{CLL}_R

It is shown that, for any equation $X=_{RS} t_X$ in the LLTS-oriented process calculus $\text{CLL}_R$, if $X$ is strongly guarded in $t_X$, then the recursive term $\langle X|X=t_X \rangle$ is the greatest solution of this equation w.r.t L\"{u}ttgen and Vogler's ready simulation.Comment: 9 pages. arXiv admin note: text overlap with arXiv:1411.075

Merging Process Algebra and Action-based Computation Tree Logic

Process algebra and temporal logic are two popular paradigms for the specification, verification and systematic development of reactive and concurrent systems. These two approaches take different standpoint for looking at specifications and verifications, and offer complementary advantages. In order to mix algebraic and logic styles of specification in a uniform framework, the notion of a logic labelled transition system (LLTS) has been presented and explored by Luttgen and Vogler. This paper intends to propose a LLTS-oriented process calculus which, in addition to usual process-algebraic operators, involves logic connectives (conjunction and disjunction) and standard temporal operators (always and unless). This calculus preserves usual properties of these logic operators, allows one to freely mix operational and logic operators, and supports compositional reasoning. Moreover, the links between this calculus and Action-based Computation Tree Logic (ACTL) including characteristic formulae of process terms, characteristic processes of ACTL formulae and Galois connection are explored.Comment: 64 page

Linear time logic control of linear systems with disturbances

The formal analysis and design of control systems is one of recent trends in control theory. In this area, in order to reduce the complexity and scale of control systems, finite abstractions of control systems are introduced and explored. In non-disturbance case, the controller of control systems is often generated from the controller of finite abstractions. Recently, Pola and Tabuada provide approximate finite abstractions for linear control systems with disturbance inputs. However, these finite abstractions and original linear systems do not always share the identical specifications, which obstructs designing controller (of linear systems) based on their finite abstractions. This paper tries to bridge such gap between linear systems and their finite abstractions.Comment: 32 pages, 4 figue

Axiomatizing L\"{u}ttgen and Vogler's ready simulation for finite processes in CLLR\text{CLL}_R

In the framework of logic labelled transition system, a variant of weak ready simulation has been presented by L\"{u}ttgen and Vogler. It has been shown that such behavioural preorder is the largest precongruence w.r.t parallel and conjunction composition satisfying desired properties. This paper offers a ground-complete axiomatization for this precongruence over processes containing no recursion in the calculus $\text{CLL}_R$. Compared with usual inference system for process calculus, in addition to axioms about process operators, such system contains a number of axioms to characterize the interaction between process operators and logical operators.Comment: 25 page

On Recursive Operations Over Logic LTS

Recently, in order to mix algebraic and logic styles of specification in a uniform framework, the notion of a logic labelled transition system (Logic LTS or LLTS for short) has been introduced and explored. A variety of constructors over LLTS, including usual process-algebraic operators, logic connectives (conjunction and disjunction) and standard temporal operators (always and unless), have been given. However, no attempt has made so far to develop general theory concerning (nested) recursive operations over LLTSs and a few fundamental problems are still open. This paper intends to study this issue in pure process-algebraic style. A few fundamental properties, including precongruence and the uniqueness of consistent solutions for equations, will be established.Comment: 66 page

A control strategy algorithm for finite alternating transition systems

Recently, there has been an increasing interest in the formal analysis and design of control systems. In this area, in order to reduce the complexity and scale of control systems, finite abstractions of control systems are introduced and explored. Amongst, Pola and Tabuada construct finite alternating transition systems as approximate finite abstractions for control systems with disturbance inputs [SIAM Journal on Control and Optimization, Vol. 48, 2009, 719-733]. Given linear temporal logical formulas as specifications, this paper provides a control strategy algorithm to find control strategies of Pola and Tabuada's abstractions enforcing specifications.Comment: 21 pages, 4 figure

A Process Calculus with Logical Operators

In order to combine operational and logical styles of specifications in one unified framework, the notion of logic labelled transition systems (Logic LTS, for short) has been presented and explored by L\"{u}ttgen and Vogler in [TCS 373(1-2):19-40; Inform. & Comput. 208:845-867]. In contrast with usual LTS, two logical constructors $\wedge$ and $\vee$ over Logic LTSs are introduced to describe logical combinations of specifications. Hitherto such framework has been dealt with in considerable depth, however, process algebraic style way has not yet been involved and the axiomatization of constructors over Logic LTSs is absent. This paper tries to develop L\"{u}ttgen and Vogler's work along this direction. We will present a process calculus for Logic LTSs (CLL, for short). The language CLL is explored in detail from two different but equivalent views. Based on behavioral view, the notion of ready simulation is adopted to formalize the refinement relation, and the behavioral theory is developed. Based on proof-theoretic view, a sound and ground-complete axiomatic system for CLL is provided, which captures operators in CLL through (in)equational laws.Comment: 52 page

Federated Learning on Non-IID Data: A Survey

Federated learning is an emerging distributed machine learning framework for privacy preservation. However, models trained in federated learning usually have worse performance than those trained in the standard centralized learning mode, especially when the training data are not independent and identically distributed (Non-IID) on the local devices. In this survey, we pro-vide a detailed analysis of the influence of Non-IID data on both parametric and non-parametric machine learning models in both horizontal and vertical federated learning. In addition, cur-rent research work on handling challenges of Non-IID data in federated learning are reviewed, and both advantages and disadvantages of these approaches are discussed. Finally, we suggest several future research directions before concluding the paper