Approaching the Coverability Problem Continuously

In this paper we focused our attention on a particular hybrid PN model called FOHPN, that is based on the fluidification of discrete PNs, and whose main feature is that the instantaneous firing speed of continuous transitions keeps constant during each macroperiod. In the first part of the paper we discuss in detail the advantages of fluidification, and provide a brief survey of the most important formalisms within the hybrid PN framework. Finally, we showed how FOHPNs can be efficiently used to model SC, and how interesting optimization problems can be solved via numerical simulation, by simply solving on-line a certain number of LPPs.

Verification of Concurrent Assembly Programs with a Petri Net Based Safety Policy

Hybrid Petri Nets (PN), combining T-timed discrete PN and continuous PN, are convenient for the modelling and the performance analysis of fluid systems or manufacturing systems such as batch or high speed production systems. For instance, the continuous process can be modelled by a continuous PN while the state of machines, up or down, can be represented by a discrete PN. The aim of the paper is to characterise the timed dynamic behaviour of continuous PN with constant speed. More precisely, the final values of the instantaneous firing speeds of continuous neutral weighted marked graph, supposed live, are determined independently of the initial marking and without using the timed evolution. Finally an application to a flow system is given.

Most verification techniques for highly populated discrete systems suffer from the state explosion problem. The "fluidification" of discrete systems is a classical relaxation technique that aims to avoid the state explosion problem. Continuous Petri nets are the result of fluidifying traditional discrete Petri nets. In continuous Petri nets the firing of a transition is not constrained to the naturals but to the non-negative reals. Unfortunately, some important properties, as liveness, may not be preserved when the discrete net model is fluidified. Therefore, a thorough study of the properties of continuous Petri nets is required. This paper focuses on the study of deadlock-freeness in the framework of mono-T-semiflow continuous Petri nets, i.e., conservative nets with a single repetitive sequence (T-semiflow). The study is developed both on untimed and timed systems. Topological necessary conditions are extracted for this property. Moreover, a bridge relating deadlock-freeness conditions for untimed and timed systems is established

This paper deals with a "digital twin" (DT) approach for processing, reprocessing, and scrapping (P/R/S) technology running on a modular production system (MPS) assisted by a mobile cyber-physical robotic system (MCPRS). The main hardware architecture consists of four line-shaped workstations (WSs), a wheeled mobile robot (WMR) equipped with a robotic manipulator (RM) and a mobile visual servoing system (MVSS) mounted on the end effector. The system architecture integrates a hierarchical control system where each of the four WSs, in the MPS, is controlled by a Programable Logic Controller (PLC), all connected via Profibus DP to a central PLC. In addition to the connection via Profibus of the four PLCs, related to the WSs, to the main PLC, there are also the connections of other devices to the local networks, LAN Profinet and LAN Ethernet. There are the connections to the Internet, Cloud and Virtual Private Network (VPN) via WAN Ethernet by open platform communication unified architecture (OPC-UA). The overall system follows a DT approach that enables task planning through augmented reality (AR) and uses virtual reality (VR) for visualization through Synchronized Hybrid Petri Net (SHPN) simulation. Timed Petri Nets (TPNs) are used to control the processes within the MPS's workstations. Continuous Petri Nets (CPNs) handle the movement of the MCPRS. Task planning in AR enables users to interact with the system in real time using AR technology to visualize and plan tasks. SHPN in VR is a combination of TPNs and CPNs used in the virtual representation of the system to synchronize tasks between the MPS and MCPRS. The workpiece (WP) visits stations successively as it is moved along the line for processing. If the processed WP does not pass the quality test, it is taken from the last WS and is transported, by MCPRS, to the first WS where it will be considered for reprocessing or scrapping.

Continuous Petri Nets (continuous-PN) have been introduced to avoid the explosion of the number of reachable states in a classical Petri Net, when this net contains a great number of tokens. This is the case of production systems, particularly a flexible manufacturing system. In a continuous-PN, the marking of a place is represented by a real number and with each transition is associated a maximum firing speed. Two kinds of modelling of manufacturing systems by continuous-PN are presented in this paper. The first one gives good results when the system is saturated (many parts). The second one works well even if the system is not saturated.

Modern multi-core processors equipped with weak memory models seemingly reorder instructions (with respect to program order) due to built-in optimizations. For concurrent programs, weak memory models thereby produce interleaved executions which are impossible on sequentially consistent (SC) memory. Verification of concurrent programs consequently needs to take the memory model of the executing processor into account. This, however, makes most standard software verification tools inapplicable.

On fluidification of Petri Nets: from discrete to hybrid and continuous models

In this paper, we study performance evaluation of workflow-based information systems. Because of state space explosion, analysis by stochastic models, such as stochastic Petri nets and queuing models, is not suitable for workflow systems in which a large number of flow instances run concurrently. We use fluid-flow approximation technique to overcome this difficulty. In the proposed method, GSPN (Generalized Stochastic Petri Nets) models representing workflows are approximated by a class of timed continuous Petri nets, called routing timed continuous Petri nets (RTCPN). In RTCPN models, each discrete set is approximated by a continuous region on a real-valued vector space, and variance in probability distribution is replaced with a real-valued interval. Next we derive piecewise linear systems from RTCPN models, and use interval methods to compute guaranteed enclosures for state variables. As a case study, we solve an optimal resource assignment problem for a paper review process.

Concurrency, as a useful feature of many modern programming languages and systems, is generally hard to reason about. Although existing work has explored the verification of concurrent programs using high-level languages and calculi, the verification of concurrent assembly code remains an open problem, largely due to the lack of abstraction at a low-level. Nevertheless, it is sometimes necessary to reason about assembly code or machine executables so as to achieve higher assurance.In this paper, we propose a logic-based "type" system for the static verification of concurrent assembly programs, applying the "invariance proof" technique for verifying general safety properties and the "assume-guarantee" paradigm for decomposition. In particular, we introduce a notion of "local guarantee" for the thread-modular verification in a non-preemptive setting.Our system is fully mechanized. Its soundness has been verified using the Coq proof assistant. A safety proof of a program is semi-automatically constructed with help of Coq, allowing the verification of even undecidable safety properties. We demonstrate the usage of our system using three examples, addressing mutual exclusion, deadlock freedom, and partial correctness respectively.

Continuous Petri nets aim to avoid the state explosion problem of classical discrete Petri nets by relaxing the integrality constraint of the firing of transitions. Although the resulting formalism can successfully model a number of features of dynamic systems, its use in complex real systems can be hindered by the limited number of possible dynamics and by the difficulty in accommodating uncertain parameters. The modeling formalism of Flexible Nets can overcome these difficulties by significantly extending the modeling and analysis possibilities of continuous Petri nets. The modeling capabilities of Flexible Nets will be presented together with their analysis possibilities in both the transient and steady state.

This work is concerned with duality of controllability and observability of Timed continuous Petri nets (TCPNs). Based on the duality definition presented in [4] for (discrete) Petri nets, a procedure for computing a dual system of a given TCPN, in a particular configuration, is provided in this work. Furthermore, it is demonstrated that the rank of the controllability matrix of a TCPN and the rank of the observability matrix of its dual are related in a precise manner. The analysis here presented can be used to translate previous results of observability analysis to controllability and vice versa.

Verification is routinely used when developing computer hardware and concurrent programs. A sequential program can always be tested and retested, but the nondeterministic nature of hardware and concurrent programs limits the effectiveness of testing as a method to demonstrate that the system is correct. Slight variations in timing, perhaps caused by congestion on a network, mean that two executions of the same program might give different results. Even if a bug is found by testing and then fixed, we have no way of knowing if the next test runs correctly because we fixed the bug or because the execution followed a different scenario, one in which the bug cannot occur.

The disassembly system considered is a plant for which a different station carries out each operation. In other words, every operation with no precedence relation is carried out in parallel. The modeling approach adopted consists in splitting the disassembly system into stations, each one having the same structure, and being represented by the same continuous Petri net. It constitutes a simple representation of the system. Under certain assumptions, this representation has allowed us to characterize analytically the stationary behavior of the system.

Defects in software cost money and sometimes lives. Even with rigorous testing, there are countless ways for programs to go wrong. Testing does not guarantee that a given program is correct for every input. Concurrent program testing does not guarantee that a program is correct for the example inputs. Formal program verification has been used as a technique to ensure program correctness for several years. It analyses the properties of the code and ensures that nothing goes wrong. In this thesis, a formal verification tool is designed and implemented based on Boogie IVL (Intermediate Verification Language) for a multi-threaded and object-oriented language named HARPO (HARdware Parallel Objects). We have designed the specific annotations intended only for use in verification. These annotations help the HARPO verifier to translate the program into an equivalent Boogie code. The resulting Boogie code is checked with theorem provers to verify the correctness of the HARPO program. Boogie code generation is tested using unit testing, and some of the case studies are reported. Consequently, programmers can use the HARPO verifier for verification of their concurrent programs.