Hierarchical Controller Synthesis Under Linear Temporal Logic Specifications Using Dynamic Quantization

Linear temporal logic(LTL)is an intuitive and expressive language to specify complex control tasks,and how to design an efficient control strategy for LTL specification is still a challenge.In this paper,we implement the dynamic quantization technique to propose a novel hierarchical control strategy for nonlinear control systems under LTL specifications.Based on the regions of interest involved in the LTL formula,an accepting path is derived first to provide a high-level solution for the controller synthesis problem.Second,we develop a dynamic quantization based approach to verify the realization of the accepting path.The realization verification results in the necessity of the controller design and a sequence of quantization regions for the controller design.Third,the techniques of dynamic quantization and abstraction-based control are combined together to establish the local-to-global control strategy.Both abstraction construction and controller design are local and dynamic,thereby resulting in the potential reduction of the computational complexity.Since each quantization region can be considered locally and individually,the proposed hierarchical mechanism is more efficient and can solve much larger problems than many existing methods.Finally,the proposed control strategy is illustrated via two examples from the path planning and tracking problems of mobile robots.

Completeness of bounded model checking temporal logic of knowledge

In order to find the completeness threshold which offers a practical method of making bounded model checking complete, the over-approximation for the complete threshold is presented. First, a linear logic of knowledge is introduced into the past tense operator, and then a new temporal epistemic logic LTLKP is obtained, so that LTLKP can naturally and precisely describe the system＇s reliability. Secondly, a set of prior algorithms are designed to calculate the maximal reachable depth and the length of the longest of loop free paths in the structure based on the graph structure theory. Finally, some theorems are proposed to show how to approximate the complete threshold with the diameter and recurrence diameter. The proposed work resolves the completeness threshold problem so that the completeness of bounded model checking can be guaranteed.

Intrusion Detection Algorithm Based on Model Checking Interval Temporal Logic

Model checking based on linear temporal logic reduces the false negative rate of misuse detection.However,linear temporal logic formulae cannot be used to describe concurrent attacks and piecewise attacks.So there is still a high rate of false negatives in detecting these complex attack patterns.To solve this problem,we use interval temporal logic formulae to describe concurrent attacks and piecewise attacks.On this basis,we formalize a novel algorithm for intrusion detection based on model checking interval temporal logic.Compared with the method based on model checking linear temporal logic,the new algorithm can find unknown succinct attacks.The simulation results show that the new method can effectively reduce the false negative rate of concurrent attacks and piecewise attacks.

Translating Linear Temporal Logic Formula s into Automata

To combat the well-known state-space explosion problem in Prop ositional Linear T emp o- ral Logic （PLTL） model checking, a novel algo- rithm capable of translating PLTL formulas into Nondeterministic Automata （NA） in an efficient way is proposed. The algorithm firstly transforms PLTL formulas into their non-free forms, then it further translates the non-free formulas into their Normal Forms （NFs）, next constructs Normal Form Graphs （NFGs） for NF formulas, and it fi- nally transforms NFGs into the NA which ac- cepts both finite words and int-mite words. The experimental data show that the new algorithm re- duces the average number of nodes of target NA for a benchmark formula set and selected formulas in the literature, respectively. These results indi- cate that the PLTL model checking technique em- ploying the new algorithm generates a smaller state space in verification of concurrent systems.

Timed automata for metric interval temporal logic formulae in prototype verification system

Based on analysis of the syntax structure and semantics model of the metric interval temporal logic （MITL） formulas, it is shown how to transform a formula written in the real-time temporal logic MITL formula into a fair timed automaton （TA） that recognizes its satisfying models with prototype verification system （PVS） in this paper. Both the tabular construction＇s principles and the PVS implementation details are given for the different type of MITL formula according to the corresponding semantics interpretations. After this transformation procedure, specifications expressed with MITL formula can be verified formally in the timed automata framework developed previously.

Model Checking over Paraconsistent Temporal Logic

Classical logic cannot be used to effectively reason about concurrent systems with inconsistencies (inconsistencies often occur, especially in the early stage of the development, when large and complex concurrent systems are developed). In this paper, we propose the use of a guasi-classical temporal logic (QCTL) for supporting the verification of temporal properties of such systems even where the consistent model is not available. Our models are paraKripke structures (extended standard Kripke structures), in which both a formula and its negation are satisfied in a same state, and properties to be verified are expressed by QCTL with paraKripke structures semantics. We introduce a novel notion of paraKripke models, which grasps the paraconsistent character of the entailment relation of QCTL. Furthermore, we explore the methodology of model checking over QCTL, and describe the detailed algorithm of implementing QCTL model checker. In the sequel, a simple example is presented, showing how to exploit the proposed model checking technique to verify the temporal properties of inconsistent concurrent systems.

A survey on temporal logics for specifying and verifying real-time systems

Over the last two decades, there has been an extensive study of logical formalisms on specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for formal specification of real-time and complex systems, an up to date survey of these logics does not exist in the literature. In this paper we analyse various temporal formalisms introduced for specification, including propositional/first-order linear temporal logics, branching temporal logics, interval temporal logics, real-time temporal logics and probabilistic temporal logics. We give decidability, axiomatizability, expressiveness, model checking results for each logic analysed. We also provide a comparison of features of the temporal logics discussed.

A Framed Temporal Logic Programming Language

We discuss the projection temporal logic (PTL), based on a primitiveprojection operator, prj. A framing technique is also presented, using which a synchronizationoperator, await, is defined within the underlying logic. A framed temporal logic programminglanguage (FTLL) is presented. To illustrate how to use both the language and framing technique, someexamples are given.

A temporal programming model with atomic blocks based on projection temporal logic

Atomic blocks, a high-level language construct that allows programmers to explicitly specify the atomicity of operations without worrying about the implementations, are a promising approach that simplifies concurrent programming. On the other hand, temporal logic is a successful model in logic programming and concurrency verification, but none of existing temporal programming models supports concurrent programming with atomic blocks yet. In this paper, we propose a temporal programming model （αPTL） which extends the projection temporal logic （PTL） to support concurrent programming with atomic blocks. The novel construct that formulates atomic execution of code blocks, which we call atomic interval formulas, is always interpreted over two consecutive states, with the internal states of the block being abstracted away. We show that the framing mechanism in projection temporal logic also works in the new model, which consequently supports our development of an executive language. The language supports concurrency by introducing a loose interleaving semantics which tracks only the mutual exclusion between atomic blocks. We demonstrate the usage of αPTL by modeling and verifying both the fine-grained and coarse-grained concurrency.

Multi-agent system motion planning under temporal logic specifications and control barrier function

In this paper,w e provide a novel scheme to solve the motion planning problem of multi-agent systems under high-level task specifications.First,linear temporal logic is applied to express the global task specification.Then an efficient and decentralized algorithm is proposed to decom pose it into local tasks.M oreover,w e use control barrier function to synthesize the local controller for each agent under the linear temporal logic motion plan with safety constraint.Finally,simulation results show the effectiveness and efficiency of our proposed scheme.

Automated Theorem Proving in Temporal Logic:T-Resolution

This paper presentes a novel resolution method, T-resolution, based on the first order temporal logic. The primary claim of this method is its soundness and completeness. For this purpose, we construct the corresponding semantic trees and extend Herbrand's Theorem.

MSVL： a typed language for temporal logic programming

The development of types is an important but challenging issue in temporal logic programming. In this paper, we investigate how to formalize and implement types in the temporal logic programming language MSVL, which is an executable subset of projection temporal logic （PTL）. Specifically, we extend MSVL with a few groups of types including basic data types, pointer types and struct types. On each type, we specify the domain of values and define some standard operations in terms of logic functions and predicates. Then, it is feasible to formalize statements of type declaration of program variables and statements of struct definitions as logic formulas. As the implementation of the theory, we extend the MSV toolkit with the support of modeling, simulation and verification of typed MSVL programs. Applications to the construction of AVL tree and ordered list show the practicality of the language.

Piecewise output feedback control for affine systems with disturbances based on linear temporal logic specifications

In the paper,we investigate the problem of finding a piecewise output feedback control law for an uncertain affine system such that the resulting closed-loop output satisfies a desired linear temporal logic (LTL) specification.A two-level hierarchical approach is proposed to solve the problem in a triangularized output space.In the lower level,we explore whether there exists a robust output feedback control law to make the output starting in a simplex either remains in it or leaves via a specific facet.In the higher level,for the triangularization,we construct the transition system according to the reachability relationship obtained in the lower level and search for feasible paths that meet the LTL specification.The control approach is then applied to solve a motion planning problem.

Formal verification with projection temporal logic

Projection temporal logic(PTL) is an extension of interval temporal logic(ITL) with a new projection operator prj and infinite intervals which has been well investigated in the past ten years.In this paper,we review the work on PTL in four aspects:(1) decidability,complexity and expressiveness of propositional PTL(PPTL);(2) modeling,simulation and verification language(MSVL);(3) formal verification approaches with MSVL and PPTL;and(4) supporting toolkit MSV.

A Structured Temporal Logic Language:XYZ/SE

In order to enhance the readability and to simplify the verification of temporal logic programs in the XYZ system,we propose a structured temporal logic language called XYZ/SE,based on XYZ/BE which is the basis language of the XYZ system.A set of proof rules are given and proved to be sound and adequate for proving the partial correctness of XYZ/SE programs in a compositional way.Moreover,we show that every XYZ/BE program can be transformed into an equivalent XYZ/SE program.So we have developed a general compositional verification method in the XYZ system concerning the sequential case.

A formal model for ledger management systems based on contracts and temporal logic

A key component of blockchain technology is the ledger,viz.,a database that,unlike standard databases,keeps in memory the complete history of past transactions as in a notarial archive for the benefit of any future test.In second-generation blockchains such as Ethereum,the ledger is coupled with smart contracts,which enable the automation of transactions associated with agreements between the parties of a financial or commercial nature.The coupling of smart contracts and ledgers provides the technological background for very innovative application areas,such as Decentralized Autonomous Organizations(DAOs),Initial Coin Offerings(ICOs),and Decentralized Finance(DeFi),which propelled blockchains beyond cryptocurrencies that were the only focus of first generation blockchains,such as Bitcoin.However,the currently used implementation of smart contracts as arbitrary programming constructs has made them susceptible to dangerous bugs that can be exploited maliciously and has moved their semantics away from that of legal contracts.We propose here to recompose the split and recover the reliability of databases by formalizing a notion of contract modeled as a finite-state automaton with well-defined computational characteristics derived from encoding in terms of allocations of resources to actors,as an alternative to the approach based on programming.To complete the work,we use temporal logic as the basis for an abstract query language that is effectively suited to the historical nature of the information kept in the ledger.

Symbolic Control of Hybrid Systems from Signal Temporal Logic Specifications

In safety-critical systems,it is desirable to automatically synthesize controllers for complex tasks with guaranteed safety and correctness.Although much progress has been made through controller synthesis from temporal logic speci-cations,existing approaches generally require conservative assumptions and do not scale well with system dimensionality.We propose a scalable,provably complete algorithm that synthesizes continuous trajectories for hybrid systems to satisfy temporal logic speci-cations.Speci-cally,we harness highly e±cient Boolean satis-ability(SAT)and Linear Programming(LP)solvers to-nd trajectories that satisfy nonconvex Signal Temporal Logic(STL)speci-cations for a class of high dimensional hybrid systems.The proposed design algorithms are proven sound and complete,and are validated in simulation experiments.

A Heuristic Method for Temporal Analysis Based on Petri Net

Reachability-based analysis and temporal analysis are used to verify the properties of concurrent systems, and it is important to exploit fast and efficient methods. This paper gives semantics of temporal formulae with edges of the transition system of Petri net, and then presents a fast temporal analyzing method, which takes advantage of both Petri net and temporal logic. The method only expands a path of equivalence trace while the path does not satisfy a property according to trace semantics of Petri net, and can validate directly the property on Petri net. Moreover, we exploit a minimal degree of in-out of a node as heuristics to select a path of an equivalence trace. Finally, we demonstrate the validity of the method that decreases state spaces and improves the verification system with the experimental results.

Application of the Constrained Predicated Nets and Interval Logic to Production Systems

A method to model and analyze the hybrid systems is presented. The time to be considered in the plant is taken as an explicit parameter through the constrained predicated net (CPN). The CPN's basic structure is a Petri net with predicated transition. All components of the net are expressed by annotation which is defined on rational set Q. The analysis method for the plant is interval temporal logic represented by Petri nets. This paper combines the above two methods to synthesize the hybrid system, gives a simple and clear expression of the expected action of the studied plant.

基于用户同意的隐私保护协议形式化描述与验证

将用户同意与访问控制相结合是解决隐私保护的主要方法之一.然而,现有的隐私保护访问控制方法仅从数据控制者的角度,不考虑个人对访问决策的参与,无法满足自主可控的需求.为了解决这个问题,本文提出了一种基于用户同意的隐私保护访问控制协议,将用户同意转化为一种同意权限,形成一种同意加授权的双重访问控制机制.本文给出协议的语法、语义及安全性定义和分析,并采用模型检测的方法对协议应满足的性质进行验证,最终证明本文的设计可以从访问控制的角度满足个人信息保护法规的要求.