Artifact Lifecycle Discovery

Artifact-centric modeling is a promising approach for modeling business processes based on the so-called business artifacts - key entities driving the company's operations and whose lifecycles define the overall business process. While artifact-centric modeling shows significant advantages, the overwhelming majority of existing process mining methods cannot be applied (directly) as they are tailored to discover monolithic process models. This paper addresses the problem by proposing a chain of methods that can be applied to discover artifact lifecycle models in Guard-Stage-Milestone notation. We decompose the problem in such a way that a wide range of existing (non-artifact-centric) process discovery and analysis methods can be reused in a flexible manner. The methods presented in this paper are implemented as software plug-ins for ProM, a generic open-source framework and architecture for implementing process mining tools

Bisimulation Relations Between Automata, Stochastic Differential Equations and Petri Nets

Two formal stochastic models are said to be bisimilar if their solutions as a stochastic process are probabilistically equivalent. Bisimilarity between two stochastic model formalisms means that the strengths of one stochastic model formalism can be used by the other stochastic model formalism. The aim of this paper is to explain bisimilarity relations between stochastic hybrid automata, stochastic differential equations on hybrid space and stochastic hybrid Petri nets. These bisimilarity relations make it possible to combine the formal verification power of automata with the analysis power of stochastic differential equations and the compositional specification power of Petri nets. The relations and their combined strengths are illustrated for an air traffic example.Comment: 15 pages, 4 figures, Workshop on Formal Methods for Aerospace (FMA), EPTCS 20m 201

Computer-aided analysis of concurrent systems

The introduction of concurrency into programs has added to the complexity of the software design process. This is most evident in the design of communications protocols where concurrency is inherent to the behavior of the system. The complexity exhibited by such software systems makes more evident the needs for computer-aided tools for automatically analyzing behavior.The Distributed Systems project at UCI has been developing a suite of tools, based on Petri nets, which support the design and evaluation of concurrent software systems. This paper focuses attention on one of the tools: the reachability graph analyzer (RGA). This tool provides mechanisms for proving general system properties (e.g., deadlock-freeness) as well as system-specific properties. The tool is sufficiently general to allow a user to apply complex user-defined analysis algorithms to reachability graphs. The alternating-bit protocol with a bounded channel is used to demonstrate the power of the tool and to point to future extensions

RGA users manual : version 2.3

RGA is an interpreter for a special language designed for the analysis of reachability graphs, or control flow graphs, generated from Petri nets. Although in some cases the reachability graph can become too large to be tractable, or can even be infinite, many interesting problems exist whose reachability graphs are of reasonable size. In RGA, the user has access to the names of the places in the net, and to the states of the reachability graph. The structure of the graph is also available through functions which return the sets of successor or predecessor states of a state and the transition-firings connecting the states. The RGA language allows dynamic typing of identifiers, recursion, and function and operator overloading. Rather than providing a number of predefined analysis functions, RGA provides primitive functions which allow the user to conduct complex analyses with little programming effort. RGA is part of a suite of tools, called P-NUT, intended to facilitate the analysis of concurrent systems described by Petri nets

Abridged Petri Nets

A new graphical framework, Abridged Petri Nets (APNs) is introduced for bottom-up modeling of complex stochastic systems. APNs are similar to Stochastic Petri Nets (SPNs) in as much as they both rely on component-based representation of system state space, in contrast to Markov chains that explicitly model the states of an entire system. In both frameworks, so-called tokens (denoted as small circles) represent individual entities comprising the system; however, SPN graphs contain two distinct types of nodes (called places and transitions) with transitions serving the purpose of routing tokens among places. As a result, a pair of place nodes in SPNs can be linked to each other only via a transient stop, a transition node. In contrast, APN graphs link place nodes directly by arcs (transitions), similar to state space diagrams for Markov chains, and separate transition nodes are not needed. Tokens in APN are distinct and have labels that can assume both discrete values ("colors") and continuous values ("ages"), both of which can change during simulation. Component interactions are modeled in APNs using triggers, which are either inhibitors or enablers (the inhibitors' opposites). Hierarchical construction of APNs rely on using stacks (layers) of submodels with automatically matching color policies. As a result, APNs provide at least the same modeling power as SPNs, but, as demonstrated by means of several examples, the resulting models are often more compact and transparent, therefore facilitating more efficient performance evaluation of complex systems.Comment: 17 figure

Performance evaluation of an emergency call center: tropical polynomial systems applied to timed Petri nets

We analyze a timed Petri net model of an emergency call center which processes calls with different levels of priority. The counter variables of the Petri net represent the cumulated number of events as a function of time. We show that these variables are determined by a piecewise linear dynamical system. We also prove that computing the stationary regimes of the associated fluid dynamics reduces to solving a polynomial system over a tropical (min-plus) semifield of germs. This leads to explicit formul{\ae} expressing the throughput of the fluid system as a piecewise linear function of the resources, revealing the existence of different congestion phases. Numerical experiments show that the analysis of the fluid dynamics yields a good approximation of the real throughput.Comment: 21 pages, 4 figures. A shorter version can be found in the proceedings of the conference FORMATS 201

Dense-Timed Petri Nets: Checking Zenoness, Token liveness and Boundedness

We consider Dense-Timed Petri Nets (TPN), an extension of Petri nets in which each token is equipped with a real-valued clock and where the semantics is lazy (i.e., enabled transitions need not fire; time can pass and disable transitions). We consider the following verification problems for TPNs. (i) Zenoness: whether there exists a zeno-computation from a given marking, i.e., an infinite computation which takes only a finite amount of time. We show decidability of zenoness for TPNs, thus solving an open problem from [Escrig et al.]. Furthermore, the related question if there exist arbitrarily fast computations from a given marking is also decidable. On the other hand, universal zenoness, i.e., the question if all infinite computations from a given marking are zeno, is undecidable. (ii) Token liveness: whether a token is alive in a marking, i.e., whether there is a computation from the marking which eventually consumes the token. We show decidability of the problem by reducing it to the coverability problem, which is decidable for TPNs. (iii) Boundedness: whether the size of the reachable markings is bounded. We consider two versions of the problem; namely semantic boundedness where only live tokens are taken into consideration in the markings, and syntactic boundedness where also dead tokens are considered. We show undecidability of semantic boundedness, while we prove that syntactic boundedness is decidable through an extension of the Karp-Miller algorithm.Comment: 61 pages, 18 figure