A survey of graph-based algorithms for discovering business processes

Algorithms of process discovery help analysts to understand business processes and problems in a system by creating a process model based on a log of the system. There are existing algorithms of process discovery, namely graph-based. Of all algorithms, there are algorithms that process graph-database to depict a process model. Those algorithms claimed that those have less time complexity because of the graph-database ability to store relationships. This research analyses graph-based algorithms by measuring the time complexity and performance metrics and comparing them with a widely used algorithm, i.e. Alpha Miner and its expansion. Other than that, this research also gives outline explanations about graph-based algorithms and their focus issues. Based on the evaluations, the graph-based algorithm has high performance and less time complexity than Alpha Miner algorithm

Waiting Nets: State Classes and Taxonomy

In time Petri nets (TPNs), time and control are tightly connected: time measurement for a transition starts only when all resources needed to fire it are available. Further, upper bounds on duration of enabledness can force transitions to fire (this is called urgency). For many systems, one wants to decouple control and time, i.e. start measuring time as soon as a part of the preset of a transition is filled, and fire it after some delay \underline{and} when all needed resources are available. This paper considers an extension of TPN called waiting nets that dissociates time measurement and control. Their semantics allows time measurement to start with incomplete presets, and can ignore urgency when upper bounds of intervals are reached but all resources needed to fire are not yet available. Firing of a transition is then allowed as soon as missing resources are available. It is known that extending bounded TPNs with stopwatches leads to undecidability. Our extension is weaker, and we show how to compute a finite state class graph for bounded waiting nets, yielding decidability of reachability and coverability. We then compare expressiveness of waiting nets with that of other models w.r.t. timed language equivalence, and show that they are strictly more expressive than TPNs

Combining Free choice and Time in Petri Nets

International audienceTime Petri nets (TPNs) are a classical extension of Petri nets with timing constraints attached to transitions , for which most verification problems are undecidable. We consider TPNs under a strong semantics with multiple enablings of transitions. We focus on a structural subclass of unbounded TPNs, where the underlying untimed net is free choice, and show that it enjoys nice properties in the timed setting under a multi-enabling semantics. In particular, we show that the questions of firability (whether a chosen transition can fire), and termination (whether the net has a non-terminating run) are decidable for this class. Next, we consider the problem of robustness under guard enlargement and guard shrinking, i.e., whether a given property is preserved even if the system is implemented on an architecture with imprecise time measurement. For unbounded free choice TPNs with a multi-enabling semantics, we show decidability of robustness of firability and of termination under both guard enlargement and shrinking

Combining Free Choice and Time in Petri Nets

International audienceTime Petri nets (TPNs) (Merlin 1974) are a classical extension of Petri nets with timing constraints attached to transitions, for which most verification problems are undecidable. We consider TPNs under a strong semantics with multiple enabling of transitions. We focus on a structural subclass of unbounded TPNs, where the underlying untimed net is free choice, and show that it enjoys nice properties under a multi-server semantics. In particular, we show that the questions of fireability (whether a chosen transition can fire), and termination (whether the net has a non-terminating run) are decidable for this class. We then consider the problem of robustness under guard enlargement (Puri et al. 2000), i.e., whether a given property is preserved even if the system is implemented on an architecture with imprecise time measurement. This question was studied for TPNs in (Akshay et al. 2016), and decidability of several problems was obtained for bounded classes of nets. We show that robustness of fireability is decidable for unbounded free choice TPNs with a multi-server semantics