A logic Petri net model for dynamic multi-agent game decision-making

Discrete event systems are modeled compactly by using Petri nets (T. Murata, 1989). Although Petri nets have powerful mathematical verification ability, in many cases, we have to construct the whole state space for verification. A reachability graph is one of the representations of the state space. Petri nets can describe huge systems compactly, but sometimes it is impossible to generate the reachability graph because of an explosion in required computational time and space. A Petri net is called a reversible net, when it can come back to the initial marking from any reachable marking. The paper considers a verification method for reversibility. An unfolding is obtained by unfolding a Petri net, and it preserves reachability information of an original net and structural analysis on it is much easier than on the original net. The article clarifies relations between unfoldings and reversibility, and provides a verification method for reversibility by using unfoldings.

How to deal with the contradiction between mass production effect and customized demand is the key problem on mass customization (MC). With the development of supply chain management, we can settle the contradiction through flexible and effective supply chain operation and it relies on rational supply chain resource integration (SCRI). However, supply chain operation in MC has special characters, mainly reflected in the random order information and the outstanding changes of collaborative benefits and risks which will influence the SCRI process and the collaborative psychology and negotiation state between two integration sides. Through analyzing the integration framework from the relations of integration input and output, this paper gives a deep analysis on multi-stage dynamic game process about SCRI in MC from the view of balancing the benefits and risks among both negotiation sides and points out that the integration is a collaborative game process. Through dividing the game process reasonably, this paper describes the game stage features and the index changes of resource individuals’ psychological expectations and appeals of their benefits and risks by fuzzy membership functions, and then puts forward a dynamic game decision method. Finally, testing by an application case, the method is feasible and effective.

This paper studies the modeling problem of event- triggered networked hybrid dynamic games (HDGs). By considering the influence of an event-triggering mechanism, the evolution process of dynamic games with hybrid characteristics is analyzed, and we point out the complexity and technical difficulties in the analysis of such a game problem. From the perspective of network science, we give a viewpoint on network-based modeling of event-triggered HDGs. On the basis of the state-space model with established, we first give the normal form of HDGs by a seven-tuple. We then establish the directed dynamic network model of HDGs for the first time, involving a graph-based tree structure form, which can well describe the distinctive features of the continuous-time and discrete-event dynamic game process on both sides, and has great advantages in evolutionary analysis. An example of the evolution of event-triggered HDGs show the innovation of the proposed model.

This paper discusses liveness verification of discrete-event systems modeled by n-safe ordinary Petri nets. A Petri net is live, if it is possible to fire any transition from any reachable marking. The verification method we propose is based on a partial order method called network unfolding. Network unfolding maps the original Petri net to an acyclic occurrence net. A finite prefix of the occurrence net is defined to give a compact representation of the original net’s reachability graph. A set of transition cycles is identified in the finite prefix. These cycles are then used to establish necessary and sufficient conditions that determine the original net’s liveness.

Deadlock/livelock problems can cause catastrophic results in flexible manufacturing systems (FMS) by forcing them to stop production processes at an unpredictable stage of production. Therefore, they must be handled properly in order to obtain flawless production in FMS. Petri net (PN) based deadlock/livelock studies for FMS have been widely carried out to obtain live PN models. When a PN model is live, this ensures that the modelled FMS is deadlock-free. Firstly, an uncontrolled (plant) PN model is constructed for the FMS suffering from deadlocks/livelocks. Then reachability graph (RG) analysis of this PN model is carried out to provide all possible reachable states of the modelled system. An RG of a PN model of an FMS suffering from deadlock/livelock problems can be split into the live zone (LZ) and the deadlock zone (DZ). The former is the set of system states considered to be legal (good), while the latter is the set of system states regarded to be illegal (bad). The LZ represents the optimal (maximally permissive) system behavior that must be provided by an optimal control policy. Generally, in PN based liveness studies, a liveness enforcing supervisor (LES) consisting of a set of control places (CP) is computed. Then the controlled (closed-loop) PN model is obtained by merging the plant PN model and the LES. If the number of reachable live states of the controlled PN model is the same as the ones that exist in the LZ, then the controlled model is optimal. Otherwise, it is suboptimal. The greater the number of live reachable states of the RG, the more products to be produced within the FMS. Therefore, the number of reachable live states of the controlled PN model is considered as a quality measure. It defines the behavioral permissiveness of the controlled model. In the literature, to verify the behavioral permissiveness of the PN models, the PN tool called INA (Integrated Net Analyzer) has been widely used. Recently, by means of INA, a method was proposed to compute the number of states within the LZ and the DZ of a given PN model suffering from deadlocks/livelocks. Unfortunately, INA cannot compute RGs of large PNs having a few millions of states. Therefore, in this paper by means of TINA (TIme petri Net Analyzer), an alternative faster and much more efficient method is proposed for the computation of the number of states within the LZ and the DZ for PN models with large RGs. In addition, in order to enable the development of new PN based deadlock prevention methods, further computations are also proposed. These include the computation of the set of states in the DZ, LZ and first met bad markings (FBMs) for a given PN model suffering from deadlocks/livelocks. The applicability and the effectiveness of the proposed methods are demonstrated by considering several well-known examples of FMS from the relevant literature.INDEX TERMS Flexible manufacturing systems (FMS), deadlock, deadlock prevention, Petri Nets (PN), liveness enforcing supervisor (LES), PN computation tools.

Behaviour Equivalent Max-Plus Automata for a Class of Timed Petri Nets

A maneuvering strategy based on motion camouflage in three-player differential game

This collection began as a conference on Modeling Rational and Moral Agents that combined two themes. First is the problematic place of morality within the received theory of rational choice. Decision theory, game theory, and economics are unfriendly to crucial features of morality, such as commitment to promises. But since morally constrained agents seem to do better than rational agents - say by co-operating in social situations like the Prisoner’s Dilemma - it is difficult to dismiss them as simply irrational. The second theme is the use of modeling techniques. We model rational and moral agents because problems of decision and interaction are so complex that there is much to be learned even from idealized models. The two themes come together in the most obvious feature of the papers: the common use of games, like the Prisoner’s Dilemma (PD), to model social interactions that are problematic for morality and rationality.’

Protecting critical infrastructure is a challenging task for security agencies all around the world, which is exacerbated by terrorism. Many infrastructures have network characteristics, such as transportation and communication systems. Therefore, it is necessary to study them from the perspective of network science. Game theory provides a suitable theoretical tool for the study of attack-defense confrontation between rational agents. Sequential game, which is more in line with the actual situation, can better analyze the confrontation in infrastructure protection. Previous models which combine network science with game theory only consider the attacker as a single type. However, in the real world, accurate information about the type of the attacker is not always available for the defender. In this paper, we apply Bayesian Stackelberg game to model the attack-defense confrontation in the case of uncertain attacker type.

Polley making involves dynamics, uncertainty, and strategy, which (although they overlap) can be regarded as separate aspects of the decision maker's problem. Analyzing equilibrium pohc1es (when all considerations are present) and determining how the equilibrium is altered (when one or more aspects ts ignored) are made possible by having an analytical tool that nests dynamics, uncertainty, and strategy and pernuts them to be included in the model in any combination. A tractable dynamic stochastic game (which is such a tool) 1s discussed, and its merits are mdtcated by means of an example of strategic tanff and tax pohc1es involving the USA and European Community.

We study the strategic similarity of game positions in two-player extensive games of perfect information by looking at the structure of their local game trees, with the aim of improving the performance of game-playing agents in detecting forcing continuations. We present a range of measures over the induced game trees and compare them against benchmark problems in chess, observing a promising level of accuracy in matching up trap states. Our results can be applied to chess-like interactions where forcing moves play a role, such as those arising in bargaining and negotiation.

A tool for verifying security properties of data is described, based on colored Petri nets. A conceptual data model for complex applications and a mandatory security model based on the principles of Bell-LaPadula are presented. The tool operates on such models, using the Petri net analysis techniques, based on the reachability graph. The absence of interference of sensitive associations, the reachability of information, and the temporal relationships among data access properties are studied, and conditions on the reachability graph are defined, to guarantee that such properties hold in the system. >

In workflow specifications, it is desirable that k customers can use a system interference-freely, so that no customer is disturbed by other activities on the same workflow. In a Petri net representation of a workflow, this corresponds to allowing initial k-markings, in which the number of tokens on each place is a multiple of k, and to require that every global activity is separable, that is, can be viewed as k individual activities, each acting as if the initial marking had one k’th of its values. In this paper, it is shown that, if \(k\ge 2\), if such a Petri net is plain, and if its reachability graph is finite, reversible, and persistent, then the latter is isomorphic to the reachability graph of a marked graph.

This paper proposes a fully expanded tree (FET) approach for one-place-unbounded Petri nets. The FET of a one-place-unbounded Petri net consists of all and only reachable markings from its initial marking. Its applications to liveness and deadlock analysis for such Petri nets are developed. The proposed method has a larger application scope than all the existing methods for them. Several examples are provided to show its superiority over the state-of-the-art methods.

As the complexity of application system for enterprises, an important challenge is to dynamically schedule and integrate the heterogeneous and distributed services or activities to work cooperatively and efficiently. An effective technology to resolve the problem is grid service. A grid service built on both grid computing and web services technologies is an extended Web service. An application system for enterprises is a grid service composition that consists of a collection of grid services related by data and control flow. Therefore, there is a need for modeling and analyzing techniques and tools for reliable and effective grid service composition. The Petri net based method is an idea approach. in this paper, we use a colored dynamic timed Petri net (CDTPN) to model the grid service composition. The definition of CDTPN for grid service and an algorithm to construct a composite service are proposed. We give a definition of reachable service graph and an algorithm for constructing the reachable service graph of CDTPN. Finally, we discuss the correctness and effectiveness of the grid service composition by analyzing the reachable service graph.