Silent Transitions Research Articles

Enjoy the silence: Analysis of stochastic Petri nets with silent transitions

Capturing stochastic behaviour in business and work processes is essential to quantitatively understand how nondeterminism is resolved when taking decisions within the process. This is of special interest in process mining, where event data tracking the actual execution of the process are related to process models, and can then provide insights on frequencies and probabilities. Variants of stochastic Petri nets provide a natural formal basis to represent stochastic behaviour and support different data-driven and model-driven analysis tasks in this spectrum. However, when capturing business processes, such nets inherently need a labelling that maps between transitions and activities. In many state of the art process mining techniques, this labelling is not 1-on-1, leading to unlabelled transitions and activities represented by multiple transitions. At the same time, they have to be analysed in a finite-trace semantics, matching the fact that each process execution consists of finitely many steps. These two aspects impede the direct application of existing techniques for stochastic Petri nets, calling for a novel characterisation that incorporates labels and silent transitions in a finite-trace semantics. In this article, we provide such a characterisation starting from generalised stochastic Petri nets and obtaining the framework of labelled stochastic processes (LSPs). On top of this framework, we introduce different key analysis tasks on the traces of LSPs and their probabilities. We show that all such analysis tasks can be solved analytically, in particular reducing them to a single method that combines automata-based techniques to single out the behaviour of interest within an LSP, with techniques based on absorbing Markov chains to reason on their probabilities. Finally, we demonstrate the significance of how our approach in the context of stochastic conformance checking, illustrating practical feasibility through a proof-of-concept implementation and its application to different datasets.

Automated modelling of discrete-event processes. Discovering Petri nets including silent transitions by classifying event traces

ABSTRACT This paper addresses the problem of automated modelling of discrete-event processes from event traces that capture the process behaviour. A novel method for building Petri nets (PN) that include silent transitions is presented. The method discovers workflow nets (WFN), a class of PN, from logs of event traces λ. The proposed approach is based on a classification of traces such that λ is partitioned into four classes: normal traces (λN), which do not involve the firing of silent transitions; skip traces (λS), redo traces (λR), and switch traces (λSW), which involve the firing of skip, redo, and switch type silent transitions, respectively. Afterwards, traces in λN are used to build a base WFN N, which may include silent transitions of type initialise and finalise. Then, N is refined by adding the silent transitions corresponding to the classes oftraces λS, λR, and λSW. The algorithms of the method have polynomial-time complexity; implementation and tests using artificial event logs are presented.

Silent transitions: Commercialization and changing customary land tenure systems in upland Laos

What happens to local institutional arrangements regarding access and use of communal land under the forces of agricultural commercialization? Taking Khwaykham village in Phongsaly province, Laos as a case study, this paper sheds light on this question as farm households in the settlement have progressively transitioned to commercial farming, specifically tea cultivation. Traditionally, farm households’ access and rights to use the land were embedded in their swidden agriculture practices. The adoption of tea has increasingly fixed land use rights, making land sticky at the household rather than communal level. How, why and with what effects this occurs are the focus of the paper. We argue that while this transition to tea cultivation has benefited – in income terms – most farm households in the village, it has also created an agrarian context for increased inequity between those households who rapidly took the opportunity from the tea boom and others who have missed out on it.

Discovering petri nets including silent transitions. A repairing approach based on structural patterns

Discovering petri nets including silent transitions. A repairing approach based on structural patterns

Observational interpretations of hybrid dynamic logic with binders and silent transitions

We extend hybrid dynamic logic with binders (for state variables) by distinguishing between observable and silent transitions. This differentiation gives rise to two kinds of observational interpretations: The first one relies on observational abstraction from the ordinary model class of a specification Sp by considering its closure under weak bisimulation. The second one uses an observational satisfaction relation for the axioms of the specification Sp, which relaxes the interpretation of state variables and the satisfaction of modal formulæ by abstracting from silent transitions. We establish a formal relationship between both approaches and show that they are equivalent under mild conditions. For the proof we instantiate the previously introduced concept of a behaviour-abstractor framework to the case of dynamic logic with binders and silent transitions. As a particular outcome we provide an invariance theorem and show the Hennessy-Milner property for weakly bisimilar labelled transition systems and observational satisfaction. In the second part of the paper we integrate our results in a development methodology for reactive systems leading to two versions of observational refinement. We provide conditions under which both kinds of refinement are semantically equivalent, involving implementation constructors for relabelling, hiding, and parallel composition.

Vanadium: strong demand in the Chinese steel industry

A method for discovering workflow nets (WFN) with silent transitions from a log of event traces λ is presented. It operates in two stages; in the first one, λ is partitioned into three classes of traces: normal traces, short abnormal traces, and long abnormal traces. In the second stage, the normal traces are processed to build a WFN that may contain transitions of type initialize and finalize; afterwards, this net is refined by adding the transitions of type skip and redo, which are determined from the short abnormal traces and the long abnormal traces respectively. Implementation and tests are presented.

Diagnosing timed automata using timed markings

We consider the problems of efficiently diagnosing (and predicting) what did (and will) happen after a given sequence of observations of the execution of a partially observable one-clock timed automaton. This is made difficult by the facts that timed automata are infinite-state systems, and that they can in general not be determinized. We introduce timed markings as a formalism to keep track of the evolution of the set of reachable configurations over time. We show how timed markings can be used to efficiently represent the closure under silent transitions of such automata. We report on our implementation of this approach compared to the approach of Tripakis (Fault diagnosis for timed automata, in: Damm, Olderog (eds) Formal techniques in real-time and fault-tolerant systems, Springer, Berlin, 2002) and provide some insight to a generalization of our approach to n-clock timed automata.

An Approach for Mining Multiple Types of Silent Transitions in Business Process

An Approach for Mining Multiple Types of Silent Transitions in Business Process

Timed hyperproperties

We study the satisfiability and model-checking problems for timed hyperproperties specified with HyperMITL, a timed extension of HyperLTL. While the satisfiability problem can be solved similarly as for HyperLTL, we show that the model-checking problem for HyperMITL, unless the specification is alternation-free, is undecidable even when very restricted timing constraints are allowed. On the positive side, we show that model checking HyperMITL with quantifier alternations is possible under certain semantic restrictions. As an intermediate tool, we give an ‘asynchronous’ interpretation of Wilke's monadic logic of relative distance (Ld↔) and show that it characterises timed languages recognised by timed automata with silent transitions.

Identifying Petri Nets with Silent Transitions by Event Traces Classification

Abstract A method for discovering workflow nets (WFN) with silent transitions from a log of event traces λ is presented. It operates in two stages; in the first one, λ is partitioned into three classes of traces: normal traces, short abnormal traces, and long abnormal traces. In the second stage, the normal traces are processed to build a WFN that may contain transitions of type initialize and finalize; afterwards, this net is refined by adding the transitions of type skip and redo, which are determined from the short abnormal traces and the long abnormal traces respectively. Implementation and tests are presented.

Behavioural and abstractor specifications revisited

In the area of algebraic specification there are two main approaches for defining observational abstraction: behavioural specifications use a notion of observational satisfaction for the axioms of a specification, whereas abstractor specifications define an abstraction from the standard semantics of a specification w.r.t. an observational equivalence relation between algebras. Earlier work by Bidoit, Hennicker, Wirsing has shown that in the case of first-order logic specifications both concepts coincide semantically under mild assumptions. Analogous results have been shown by Sannella and Hofmann for higher-order logic specifications and recently, by Hennicker and Madeira, for specifications of reactive systems using a dynamic logic with binders. In this paper, we bring these results into a common setting: we isolate a small set of characteristic principles to express the behaviour/abstractor equivalence and show that all three mentioned specification frameworks satisfy these principles and therefore their behaviour and abstractor specifications coincide semantically (under mild assumptions). As a new case we consider observational modal logic where observational satisfaction of Hennessy–Milner logic formulae is defined “up to” silent transitions and observational abstraction is defined by weak bisimulation. We show that in this case the behaviour/abstractor equivalence can only be obtained, if we restrict models to weakly deterministic labelled transition systems.

Qualitative Assessment of the Exceeding Behaviour of Discovered Petri Nets

In this paper, the precision evaluation of a subclass of Petri nets, called workflow nets (WFN), is addressed. A novel technique for qualitatively assessing the precision is proposed; it estimates the exceeding language of a sound WFN including cycles and silent transitions with respect to the actual language provided by the events log. The estimation, which does not consider the frequency of traces in the log, involves three sub-metrics dealing with a) activity completeness, b) finite behaviour of the model, and c) cyclic behaviour of the model. The compound metric is computed through a partial reachability graph called log-based marking graph (LMG); it is iteratively evaluated by simulating the WFN and adding new behaviour to such a LMG until the computed value converges asymptotically. The proposed technique provides a good approximation to the precision of sound WFNs modelling finite or infinite languages.

Collapsible Pushdown Automata and Recursion Schemes

We consider recursion schemes (not assumed to be homogeneously typed , and hence not necessarily safe ) and use them as generators of (possibly infinite) ranked trees. A recursion scheme is essentially a finite typed deterministic term rewriting system that generates, when one applies the rewriting rules ad infinitum , an infinite tree, called its value tree . A fundamental question is to provide an equivalent description of the trees generated by recursion schemes by a class of machines. In this article, we answer this open question by introducing collapsible pushdown automata (CPDA), which are an extension of deterministic (higher-order) pushdown automata. A CPDA generates a tree as follows. One considers its transition graph, unfolds it, and contracts its silent transitions, which leads to an infinite tree, which is finally node labelled thanks to a map from the set of control states of the CPDA to a ranked alphabet. Our contribution is to prove that these two models, higher-order recursion schemes and collapsible pushdown automata, are equi-expressive for generating infinite ranked trees. This is achieved by giving effective transformations in both directions.

A Discussion on Fault detection for a class of Hybrid Petri Nets

This paper is about fault detection for hybrid dynamical systems modeled with Partially Observed Timed Hybrid Petri Nets (POTHPNs). The marking of some continuous places and the firing of some discrete transitions are assumed to be measured on-line. Abrupt faults are considered as unexpected firings of some discrete silent transitions. From the collected measurements, a fault detection approach is proposed that combines residual design based on continuous time observers with a discrete diagnosis method based on the computation of all discrete trajectories that are consistent with the measurements. The method is suitable for the class of hybrid systems that concerns continuous processes driven by discrete controllers.

Marking Observer in Labeled Petri Nets With Application to Supervisory Control

In this paper, we consider the problem of marking estimation in labeled Petri nets whose initial marking is known to belong to a given convex set, in the presence of silent transitions (i.e., transitions labeled with the empty word) and indistinguishable transitions (i.e., transitions sharing the same label with other transitions). First, we demonstrate that all sets of markings consistent with a given sequence of observations can be described in linear algebraic terms (as a union of convex sets); subsequently, this observation is used to construct (offline) a marking observer under appropriate boundedness assumptions. Using the marking observer we show how to derive, at design time, a state feedback control law under the assumption that all transitions sharing a label can be enabled or disabled simultaneously as a group; this way, the most burdensome part of the computations is performed offline.

Bounded determinization of timed automata with silent transitions

Deterministic timed automata are strictly less expressive than their non-deterministic counterparts, which are again less expressive than those with silent transitions. As a consequence, timed automata are in general non-determinizable. This is unfortunate since deterministic automata play a major role in model-based testing, observability and implementability. However, by bounding the length of the traces in the automaton, effective determinization becomes possible. We propose a novel procedure for bounded determinization of timed automata. The procedure unfolds the automata to bounded trees, removes all silent transitions and determinizes via disjunction of guards. The proposed algorithms are optimized to the bounded setting and thus are more efficient and can handle a larger class of timed automata than the general algorithms. We show how to apply the approach in a fault-based test-case generation method, called model-based mutation testing, that was previously restricted to deterministic timed automata. The approach is implemented in a prototype tool and evaluated on several scientific examples and one industrial case study. To our best knowledge, this is the first implementation of this type of procedure for timed automata.

Probabilistic Marking Estimation in Labeled Petri Nets

Given a labeled Petri net, possibly with silent transitions, we are interested in performing current marking estimation in a probabilistic setting. We assume a known initial marking or a known finite set of initial markings, each with some a priori probability, and our goal is to obtain the conditional probabilities of possible current markings, conditioned on an observed sequence of labels. Under the assumptions that (i) the reachability set of the unobservable subnet of the given Petri net (starting from any possible initial state) is bounded (i.e., it has a finite number of reachable states), and (ii) a characterization of the a priori probabilities for occurrence of each transition enabled at each reachable marking is available, we develop a recursive algorithm that can perform current marking estimation online to efficiently obtain the probabilities of current states (conditioned on a sequence of observations). The proposed algorithm can be used in conjunction with a variety of supervisory control and fault diagnosis algorithms, in order to relax stringent constraints imposed by existing methodologies that typically rely solely on binary information regarding the possibility or impossibility of current states (but not their probabilities).

Diagnosability of Discrete-Event Systems Using Labeled Petri Nets

In this paper, we focus on labeled Petri nets with silent transitions that may either correspond to fault events or to regular unobservable events. We address the problem of deriving a procedure to determine if a given net system is diagnosable, i.e., the occurrence of a fault event may be detected for sure after a finite observation. The proposed procedure is based on our previous results on the diagnosis of discrete-event systems modeled with labeled Petri nets, whose key notions are those of basis markings and minimal explanations, and is inspired by the diagnosability approach for finite state automata proposed by Sampath in 1995. In particular, we first give necessary and sufficient conditions for diagnosability. Then, we present a method to test diagnosability that is based on the analysis of two graphs that depend on the structure of the net, including the faults model, and the initial marking.

Flexible Surface Model Explains Time-Resolved Uv-Visible Studies of Rhodopsin Activation in a Membrane Lipid Environment

Rhodopsin is the quintessential GPCR--the UV/Visible absorbance of its bound chromophore provides detailed time-resolved information about the GPCR activation steps [1]. At least four species equilibrate on the millisecond time scale after rhodopsin photoexcitation in a membrane environment [2]. The first millisecond-time scale equilibrium is between the protonated Schiff base (PSB) species Meta I480 and the deprotonated SB species Meta IIa and is pH independent. Subsequent equilibria involve spectrally silent transitions of Meta IIa to produce Meta IIb and protonation of Glu134 of the E(R)Y sequence in Meta IIb to give Meta IIbH+ where pKa describes the acid-base equilibrium. We used time-resolved absorbance measurements on the microsecond-to-hundred millisecond time scale to study effects of the membrane lipid environment on the first equilibrium constant, K1, and on the pKa of the final equilibrium. Reconstituted membranes of rhodopsin with POPC, DOPC, or DOPC/DOPE mixtures were studied at 30oC. Results were analyzed by singular value decomposition and globally fit to a sum of exponential terms. We discovered a striking increase in K1 due to either PE head groups or increased acyl chain unsaturation; by contrast pKa changed little. According to the flexible surface model (FSM), there is competition between the curvature elastic energy and the hydrophobic mismatch at the proteolipid boundary that explains the above influences of lipid-protein interactions [3]. The fact that both the lipid acyl chains and polar head groups affect the Meta I-Meta II transition of rhodopsin is a striking illustration of how protein energetics in membranes are governed by chemically nonspecific properties of the lipid bilayer. [1] J. Epps et al. (2006) Photochem. Photobiol.82, 1436-1441. [2] E. Zaitseva et al. (2010) JACS132, 4815-4821. [3] A.V. Botelho et al. (2006) BJ91, 4464-4477.

Weak bisimulation is sound and complete for [formula omitted

We investigate weak bisimulation of probabilistic systems in the presence of nondeterminism, i.e. labelled concurrent Markov chains (LCMC) with silent transitions. We develop an approach based on allowing convex combinations of computations, similar to Segala and Lynch’s use of randomized schedulers. The definition of weak bisimulation destroys the additivity property of the probability distributions, yielding instead capacities. The mathematics behind capacities naturally captures the intuition that when we deal with nondeterminism we must work with bounds on the possible probabilities rather than with their exact values. Our analysis leads to three new developments: • We identify a characterization of “image finiteness” for countable-state systems and present a new definition of weak bisimulation for these LCMCs. We prove that our definition coincides with that of Philippou, Lee and Sokolsky for finite state systems. • We show that bisimilar states have matching computations. The notion of matching involves convex combinations of transitions. • We study a minor variant of the probabilistic logic pCTL ∗ – the variation arises from an extra path formula to address action labels. We show that bisimulation is sound and complete for this variant of pCTL ∗ . This is an extended complete version of a paper that was presented at CONCUR 2002.