Extended Stochastic Petri Nets for Model-Based Design of Wetlab Experiments

We investigate the decidability of termination, reachability, coverability and deadlock-freeness of Petri nets endowed with a hierarchy of places, and with inhibitor arcs, reset arcs and transfer arcs that respect this hierarchy. We also investigate what happens when we have a mix of these special arcs, some of which respect the hierarchy, while others do not. We settle the decidability status of the above four problems for all combinations of hierarchy, inhibitor, reset and transfer arcs, except the termination problem for two combinations. For both these combinations, we show that deciding termination is as hard as deciding the positivity problem on linear recurrence sequences -- a long-standing open problem.

1.1 Relationship between Petri net and linear logic Petri nets were first introduced by Petri in his seminal Ph.D. thesis, and both the theory and the applications of his model have flourished in concurrency theory (Reisig & Rozenberg, 1998a; Reisig & Rozenberg, 1998b). The relationships between Petri nets and linear logics have been studied by many researchers (Engberg & Winskel, 1997; Farwer, 1999; Hirai, 2000; Hirai 1999; Ishihara & Hiraish, 2001; Kamide, 2004, Kamide, 2006; Kanovich, 1995; Kanovich 1994; LarcheyWendling & Galmiche, 1998; Larchey-Wendling & Galmiche, 2000; Lilius, 1992; Mart -Oliet & Meseguer, 1991; Okada, 1998; Tanabe, 1997). A category theoretical investigation of such a relationship was given by Mart -Oliet and Meseguer (Mart -Oliet & Meseguer, 1991), purely syntactical approach using Horn linear logic was established by Kanovich (Kanovich, 1995; Kanovich 1994), a naive phase linear logic for a certain class of Petri nets was given by Okada (Okada, 1998), a linear logical view of object Petri nets were studied by Farwer (Farwer, 1999), and various Petri net interpretations of linear logic using quantale models were obtained by Ishihara and Hiraishi (Ishihara & Hiraish, 2001), Engberg and Winskel (Engberg & Winskel, 1997), Larchey-Wendling and Galmiche (Larchey-Wendling & Galmiche, 1998; Larchey-Wendling & Galmiche, 2000), and Lilius (Lilius, 1992). Petri net interpretations using Kripke semantics for various fragments and extensions of intuitionistic linear logic were studied by Kamide (Kamide, 2004; Kamide, 2006c). In (Kamide, 2004), Petri net interpretations of various fragments of a spatio-temporal soft linear logic were discussed. In (Kamide, 2006c), Petri nets with inhibitor arcs, which were first introduced by Kosaraju (Kosaraju, 1973) to show the limitation of the usual Petri nets, were described using Kripke semantics for intuitionistic linear logic with strong negation. The approarches using Kripke semantics can obtain a very simple correspondence between Petri net and linear logic.

In this paper we present a survey on methods for the synthesis of Petri nets from behavioral descriptions given as languages. We consider place/transition Petri nets, elementary Petri nets and Petri nets with inhibitor arcs. For each net class we consider classical languages, step languages and partial languages as behavioral description. All methods are based on the notion of regions of languages. We identify two different types of regions and two different principles of computing from the set of regions of a language a finite Petri net generating this language. For finite or regular languages almost each combination of Petri net class, language type, region type and computation principle can be considered to compute such a net. Altogether, we present a framework for region-based synthesis of Petri nets from languages which integrates almost all known approaches and fills several remaining gaps in literature.

This article addresses expressiveness problems for Petri nets and their useful extension for modeling and control of a system that can be modeled with Petri nets. We construct some Petri net modules, namely, an enabling module, an inhibitor module and a Modulo-N counter, which are useful for system operations. We also present the simplifications for the enabling and inhibitor modules. Then, we propose two new types of arcs, namely, enabling and inhibitor arcs, with a weighted function set. The arcs with the weighted function set from places to transitions are the marked arcs. A function set is employed to denote the weight of an arc according to the system requirements. They are very useful to solve the resource reallocation problem in a resource allocation system, where resource sharing contributes to the occurrences of deadlocks. Finally, two examples are used to show the advantages of the presented new types of arcs.

Farm bill legislation directed at agricultural commodities contributes to economies of rural areas. This research quantifies the economic impacts of the Georgia cotton industry for the U.S. economy. A cotton industry model with cotton and peanut acreage is utilized with IMPLAN to estimate impacts. The Georgia cotton industry creates 4% more tax revenues for federal, state, and local governments than it receives in commodity support payments. Stochastic simulation analysis indicates that the Georgia cotton industry is not likely to remain viable without government payments. Georgia cotton production has steadily increased since 1990, and now ranks second in farm gate value among all Georgia agricultural commodities. The 2005 farm gate value for cotton totaled more than $723 million, which was first among row crops, followed by peanuts at $423 million (Boatwright and McKissick, 2006). Data from the USDA’s National Agricultural Statistics Service (NASS) show that in 2006, Georgia planted 1.4 million acres of upland cotton and ranks second after the 6.4 million acres planted in Texas. Georgia’s 2006 peanut acreage planted of 580,000 acres leads the nation and represents 45% of the U.S. total. Government payments in the form of marketing assistance payments set forth by the commodity provisions of the Farm Security and Rural Investment (FSRI) Act of 2002 are included in the farm gate value. Additional income support known as direct and countercyclical payments (DCP) can also be attributed to cotton and peanuts, though these are not included in the individual commodity farm gate values. These payments are decoupled from production in the sense that historical base acres and program yields are used to calculate support levels. Direct payments are guaranteed

With this contribution, we aim to draw a comprehensive classification of Petri nets with stopwatches w.r.t. expressiveness and decidability issues. This topic is too ambitious to be summarized in a single paper. That is why we present our results in two different parts. The scope of this first paper is to address the general results that apply for both dense-time and discrete-time semantics. We study the class of bounded Petri nets with stopwatches and reset arcs (rSwPNs), which is an extension of T-time Petri nets (TPNs) where time is associated with transitions. Stopwatches can be reset, stopped and started. We give the formal dense-time and discrete-time semantics of these models in terms of Transition Systems. We study the expressiveness of rSwPNs and its subclasses w.r.t. (weak) bisimilarity (behavioral semantics). The main results are following: 1) bounded rSw- PNs and 1-safe rSwPNs are equally expressive; 2) For all models, reset arcs add expressiveness. 3) The resulting partial classification of models is given by a set of relations explained in Fig. 7: in the forthcoming paper, we will complete these results by covering expressiveness and decidability issues when discrete-time nets are considered. For the sake of simplicity, our results are explained on a model such that the stopwatches behaviors are expressed using inhibitor arcs. Our conclusions can however be easily extended to the general class of Stopwatch Petri nets.

As automated manufacturing systems become more complex, the need for an effective design tool to produce both high-level discrete event control systems (DECS) and low-level implementations becomes more important. Petri nets represent the most effective method for both the design and implementation of DECSs. In this paper, automation Petri nets (APN) are introduced to provide a new method for the design and implementation of DECSs. The APN is particularly well suited to multiproduct systems and provides a more effective solution than Grafcet in this context. Since ordinary Petri nets do not deal with sensors and actuators of DECSs, the Petri net concepts are extended, by including actions and sensor readings as formal structures within the APN. Moreover, enabling and inhibitor arcs, which can enable or disable transitions through the use of leading-edge, falling-edge and level of markings, are also introduced. In this paper, the methodology is explained by considering a fundamental APN structure. The conversion of APNs into the IEC1131-3 ladder diagrams (LD) for implementation on a PLC is also explained by using the token passing logic (TPL) concept. Finally, an illustrative example of how APNs can be applied to a discrete manufacturing problem is described in detail.

Workflow nets (WF-nets) are Petri nets which represent workflows. Soundness is a criterion of logical correctness defined for WF-nets. It is known that soundness verification is intractable. In this paper, we propose a method to verify soundness using a Linear Temporal Logic (LTL) model checking tool, SPIN. We give an LTL necessary and sufficient condition to verify soundness for WF-nets without livelock. Acyclic WF-nets have no livelock, but cyclic WF-nets may have livelock. We also give a necessary and sufficient condition to verify livelock. Meanwhile, we show that any LTL model checking tool cannot verify soundness for WF-nets with livelock. We give necessary conditions to verify soundness for them. Those conditions enable us to use SPIN even if a given WF-net has livelock. We also develop a tool to verify soundness based on our method. We show effectiveness of our method by comparing our tool with existing soundness verification tools on verification time for 200 cyclic ACWF-nets.

In this paper, a state avoidance controller with inhibitor arcs, called IA-controller, is proposed for nonconvex forbidden state problems in Petri nets. The forbidden condition is transformed into non-convex marking constraints in controlled PNs. Simple formulas for IA-controllers are developed to avoid the non-convex marking condition. By extending enabling rule of controllable transitions, the IA-controller can realize OR-logics, which is impossible in ordinary PN structure-type controllers. The significance of IA-controller is that the controller can be easily implemented in the plant model. In addition, IA-controllers are synthesized in a modular way in order to solve multiple forbidden conditions.

Relating SPO and DPO graph rewriting with Petri nets having read, inhibitor and reset arcs

Extended labeled Petri nets (ELPNs), i.e., labeled Petri nets with inhibitor arcs, are usually used to model the desired closed-loop behavior of a controlled discrete-event system, and, as such, their states are formed with both the controller and the plant states. However, the control logic is based on the controller states only and the interaction between controller and plant is carried out through sensor readings from the plant and control actions (forced events) from the controller. This makes ELPN not suitable for modeling the controller. Control interpreted Petri nets (CIPNs), on the other hand, include control actions in the places and sensor readings in the transitions as part of their formal structure, and so provide a better formalism for controller modeling. In this paper, we propose a two-step approach to discrete-event controller implementation, as follows: (i) we first propose a set of transformation rules to convert the initial ELPN to an equivalent CIPN, therefore extracting the control logic from the desired closed-loop behavior and (ii) we present a straightforward systematic way to translate the CIPN into a ladder diagram. We apply the results presented here to the implementation of the automation system of a plastic molding machine.

We introduce the notion of net-slice to describe a subnet of a marked Petri net Σ that approximates σ's temporal behaviour with respect to a set of places P. We consider slices Σ′ whose set of places comprises the places referred to by a CTL* formula φ. If Σ is fair w.r.t. the transitions of a slice, φ |= φ can be verified and falsified by examining the slice, given φ is a CTL* formula built without using the next-time operator. Verification of LTL-X formulas is thus possible under these very weak fairness assumptions, though LTL formulas using next-time can be falsified.

Student-Friendly Coverage of Probability, Statistical Methods, Simulation, and Modeling ToolsIncorporating feedback from instructors and researchers who used the previous edition, Probability and Statistics for Computer Scientists, Second Edition helps students understand general methods of stochastic modeling, simulation, and data analysis; make o

This paper presents a basic introduction to some popular stochastic analysis methods from an unbiased disciplinary perspective. Examples ranging from fields as diverse as defense analysis, cognitive science, and instruction are illustrated throughout to demonstrate the variety of applications that benefit from such stochastic analysis methods and models. Two applications of longitudinal stochastic analysis methods to collaborative and cognitive training environments are discussed in detail. The first application applies a combination of latent mixed Markov modeling and multidimensional scaling for modeling, analyzing, and supporting the process of online knowledge sharing. In the second application, a combination of iterative nonlinear machine learning algorithms is applied to identify latent classes of problem-solving strategies. The examples illustrated in this paper are instances of an increasing global trend toward interdisciplinary research. As this trend continues to grow, research that takes advantage of the gaps and overlaps in analytical methodologies between disciplines will save time, effort, and research funds.

High-accuracy hull iteration method for uncertainty propagation in fluid-conveying carbon nanotube system under multi-physical fields