Detecting Infeasible Traces in Process Models

Zhaoxia Wang

1,2,3,4,5

, Lijie Wen

1,3,4

, Xiaochen Zhu

1,2,3,4

, Yingbo Liu

1,3,4

and Jianmin Wang

1,3,4

School of Software, Tsinghua University, Beijing 100084, China

Department of Computer Science & Technology, Tsinghua University, Beijing 100084, China

Key Lab for Information System Security, Ministry of Education, Beijing 100084, China

National Laboratory for Information Science and Technology, Beijing 100084, China

Logistical Engineering University, Chongqing 400016, China

Keywords:

Infeasible Traces, Process Models, Workﬂow Analysis.

Abstract:

Workﬂow testing is an important method of workﬂow analysis in design time. A challenging problem with

trace-oriented test data generation in particular and trace-based workﬂow analysis in general is the existence

of infeasible traces for which there is no input data for them to be executed. In this paper we build on the

theory of workﬂow nets and introduce workﬂow nets where transitions have conditions associated with them.

We then demonstrate that we can determine which execution traces, that are possible according to the control-

ﬂow dependencies, are actually possible taking the data perspective into account. This way we are able to

more accurately determine in design time the infeasible traces caused by the correlation between transition

conditions along this trace. Finally, we provide a solution to automatically detecting the shortest infeasible

trace.

1 INTRODUCTION

Workﬂow testing is an important method of workﬂow

analysis in design time (van der Aalst and ter Hofst-

ede, 2000). However, test data generation is an ex-

tremely complicated and time-consuming task as it

requires a careful analysis and understanding of the

source code and knowledge of the underlying con-

cepts of the testing criterion. For this reason, automa-

tion of test data generation may provide a signiﬁcant

cost and time reduction for workﬂowtesting. In trace-

oriented test data generation, a set of traces is selected

which satisﬁes one or more coverage criteria and test

data are generated to exercise these traces. A chal-

lenging problem with trace-oriented test data genera-

tion in particular and trace-based workﬂowanalysis in

general is the existence of infeasible traces for which

there is no input data for them to be executed. In this

case, considerable effort might be wasted in trying to

generate data for infeasible traces.

In software engineering domain, detection of

branch condition and branch correlation is a kind of

important methods in path feasibility analysis(Ngo

and Tan, 2008). Here, inspired by the approaches of

detecting the infeasible paths in software engineering

domain we propose an approach to detect the infeasi-

ble traces in process model.

For instance, for the simpliﬁed example model for

loan process (shown in Figure 1), the traces t

)∗

and t

) ∗t

become infeasible when

transition conditions are taken into account. The rea-

son of traces t

) ∗ t

non-existing is that

the conjunctive transition conditions c

∧c

on transi-

tion t

along t

)∗t

are not satisﬁed, they

are then non-executable (that is, they are infeasible

traces).

In this paper, we build on the theory of work-

ﬂow nets and introduce workﬂow nets where transi-

tions have conditions associated with them. This way

we are able to more accurately determine in design

time the infeasible traces caused by the correlation be-

tween transition conditions.

The rest of this paper is organized as follows. First

a formal deﬁnition of workﬂow nets with transition

conditions or WTC-nets for short is given and we pro-

pose a reachability analysis approach based on the

behavioural semantic of WTC-nets to detect the in-

feasible traces in process models (Section 2). We im-

plement a tool to support the proposed approach and

this tool is used to apply the approach to a number of

real-life models (Section 3). Section 4 discusses the

related work and Section 5 concludes the paper.

212

Wang Z., Wen L., Zhu X., Liu Y. and Wang J..

Detecting Infeasible Traces in Process Models.

DOI: 10.5220/0003989002120217

In Proceedings of the 14th International Conference on Enterprise Information Systems (ICEIS-2012), pages 212-217

ISBN: 978-989-8565-12-9

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

]

w: d

The set of condition variables

: info_complete d

: loan amount d

: risk

The set of transitions T

: receive_application t

: verify_application t

: modify_application

: check_loan amount t

: check risk t

: modify-loan

: approve by manager t

: approve by officer t

, t

: silent task

w: d

]

w: d

The set of conditions

: ¬d

: d

>50,000 c

: d

<=50,000 c

: d

: ¬d

Figure 1: A workﬂow model for the simpliﬁed loan process.

2 PRELIMINARIES

In this section we brieﬂy introduce workﬂow nets

with transition conditions (for short, WTC-nets).

WTC-nets are based on Petri nets and workﬂow nets.

In order to make the paper self-contained, some well-

known deﬁnitions are introduced ﬁrst.

2.1 Background

Below, we deﬁne Petri nets ﬁrst. For an overview of

Petri nets and an extensive bibliography the reader is

referred to (Murata, 1989).

Deﬁnition 1 (Petri net). A Petri net N is a tuple

(P,T, F) where P is a ﬁnite set of places, T is a ﬁ-

nite set of transitions such that P∩T = ∅, P∪T 6= ∅,

and F ⊆ (P× T) ∪ (T × P) is the ﬂow relation.

For each node x, i.e. a place or a transition, we

use •x to denote its pre-set - the set of nodes which

are input of x - i.e. •x = {y|(y, x) ∈ F}, and x• for its

post-set - the set of nodes which are output of x - i.e.

x• = {y|(x, y) ∈ F}.

Deﬁnition 2 (Marking). Let N = (P, T, F) be a Petri

net, a marking M of N is a function from its places to

the set of natural numbers, i.e. M : P → N.

Transitions can change the marking of a Petri net

if they are ﬁred. van der Aalst deﬁnes workﬂow nets

by imposing certain syntactical restrictions on Petri

nets (van der Aalst, 1998).

Deﬁnition 3 (Workﬂow net). A Workﬂow net P is a

Petri net (P, T, F) such that there is a unique source

place i, •i = ∅, a unique sink place o, o• = ∅, and

such that every node x ∈ P∪ T is on a path from i to

The initial marking for a workﬂow net, or WF-

net for short, corresponds to one token in its initial

place and thus formally corresponds to i. The desired

ﬁnal marking is the marking that has one token in the

output place o and no tokens in any other places.

2.2 Workﬂow Nets with Transition

Conditions

Central to WTC-nets is the notion of a condition. Here

we only informally describe condition class cond. A

condition c is an instance of cond.

The expression form of the class cond is a logical

expression. The operators used in cond include com-

parison operators (eg. le, leq, ge, geq,eq), arithmeti-

cal operators (eg. plus, minus, times, frac, mod, div),

boolean operators (eg. neg, and, or, implies). The data

type in cond contains int, real and bool. For a vari-

able v used in a cond, the domain of v is a set of val-

ues that v can hold. The notion var is used as the set

of all variables as well as the notion VAR is used as the

set of all possible assignments of types to varianbles.

In addition, function V

var

() is applied to a condition

to yield the variables that are used in this condition.

A WF-net with transition conditions, or WTC-net

for short, is a WF-net where the transitions are as-

signed conditions. We give an assumption that the

variables that a transition can write to, may take on

any value as a result of its execution.

Deﬁnition 4 (Workﬂow net with transition condi-

tions). A workﬂow net with transition conditions W

is a tuple (P ,V,C, G,W, TV), such that:

• P = (P, T, F) is a WF-net;

• V ⊆ var is a set of net variables;

DetectingInfeasibleTracesinProcessModels

213

• C ⊆ cond is a set of transition conditions with

∪

c∈C

var

• G : T → C is a function assigning conditions to

transitions;

• W : T → 2

is a function that yields the variables

that transitions can write to;

• TV ∈ VAR is a function assigning a type to each

net variable.

Deﬁnition 5 (Marking of WTC-net). For a WTC-

net W = (P ,V,C, G,W, TV), a marking M is a tu-

ple (M, σ), where M is a marking of WF-net P , and

σ ∈ T

∗

is a sequence of transitions.

The initial marking of this net M

is deﬁned as

(i, ε), where i is the unique source place of W , ε is

empty sequence.

Subsequently we formally deﬁne whether transi-

tion condition is satisﬁed in the context of a particular

assignment of values to variables. Given an assign-

ment as an environment e and the set of all possible

environments as ENV. The set of all possible values

is denoted as Val and it is deﬁned as the union of all

integers, reals, and booleans, i.e. Val = Z ∪ R ∪ B.

Deﬁnition 6 (Satisﬁability of conditions). Let TV :

var → Types be an assignment of types to variables

and let c be a condition in the context of type as-

signment TV, i.e., c ∈ cond, e : var → Val an as-

signment of values to variables, and the function

holds

: cond × ENV → bool can be applied to deter-

mine whether in the context of a given environment a

condition holds.

In order to evaluate if in the context of a transition

sequence σ a given transition condition φ hold, we

need to take into account the variables that are used

in the transition conditions of transitions in σ and in

φ as well as the order in which variables may be writ-

ten by transitions in σ. To solve this problem, we in-

troduce fresh variables as replacements for variables

used in transition conditions of transitions whenever

it turns out that these variables could have received a

new value through the execution of preceding transi-

tions. Fresh variables in a transition sequence σ take

the form v

where t is a transition which could write

v, i.e. v ∈ W(t), and n is a natural number, which for

a particular occurrence of transition t in σ represents

the number of previous occurrences of t in σ (this is

required in order to be able to deal with loops). We

assume that variables of the form v

do not occur as

net variables in a WTC-net, so that indeed they will

be fresh whenever introduced. We also assume that

given a renaming function ψ : var ֌ var and a con-

dition c ∈ cond, c[ψ] denotes condition c where for

every variable v ∈ V

var

(c)∩ dom(ψ) each of its occur-

rences has been replaced by ψ(v).

Deﬁnition 7 (Conjunctive transition conditions). Let

W = (P ,V,C, G,W, TV) be a WTC-net, σ ∈ T

∗

transition sequence (possibly empty, i.e. σ = ε), ψ :

var ֌ var a renaming of variables, G(t)[ψ] chang-

ing transition condition according to this renaming,

n : T → N an assignment of natural numbers to transi-

tions, and b is any boolean expression. The conjunc-

tive transition conditions along sequence with vari-

ables renaming ρ

ψ, n

(σ, b) is deﬁned by:

ψ, n

(ε, b) = b

ψ, n

(tσ, b) = ρ

′

, n

′

(σ, b∧ G(t)[ψ]) where

′

= ψ ⊕ {(v, v

n(t)

) | v ∈ W(t)} and n

′

= n⊕

{(t, n(t) + 1)}

We are now in a position to formally deﬁne when

a transition in a WTC-net is enabled in the context of

a given marking.

Deﬁnition 8 (Enabled transition in WTC-net). Let

W = (P ,V,C, G,W, TV) be a WTC-net, M = (M, σ)

be a marking of this net, and t ∈ T a transi-

tion in this net. Let b be a conjunctive transition

conditions with variables renaming deﬁned by b =

∅, {(t, 0) | t∈T}

(σ,true). Transition t is enabled in

marking M , M [t >, iff an environment e : V

var

(b) →

Val can be found such that V

holds

(b, e, TV).

Deﬁnition 9 (Firing). Let W = (P ,V,C, G,W, TV) be

a WTC-net, M = (M, σ) be a marking of this net,

and t ∈ T an enabled transition. Firing transition t

in marking M results in marking M

′

= (t • ∪(M\ •

t), σt). As per usual, we write M

→ M

′

Table 1: Deriving the conjunctive form of transition condi-

tions along sequence t

for WTC-net in Figure 1.

TCT

CTC

, d

¬d

∧ d

Transition Sequence.

Variable Renaming.

Transition Condition Transformation.

Conjunctive Transition Conditions.

Example. Assuming for the WTC-net sample in

the Figure 1, given a current marking (p

let us consider transition t

can be enabled or not.

Firstly, we observe how to derive the conjunctive

form of transition conditions for transition t

along

the sequence t

. As shown in the ﬁrst col-

umn of Table 1, variable d

is written twice by tran-

sition t

. Once each writing operation happens, d

ICEIS2012-14thInternationalConferenceonEnterpriseInformationSystems

214

is mapped into a new fresh variable as shown in the

second column of Table 1. For example, variable d

is mapped into d

and d

respectively along the

sequence t

. The corresponding transition con-

dition is then changed based on the closest preced-

ing variable renaming as shown in the third column

in Table 1. For instance, the transition condition of

transition t

in the sequence is changed as ¬d

fol-

lowing the closest preceding variable renaming d

The fourth column in Table 1 describes the dynamic

evolution of the conjunctive form of transition condi-

tions along the sequence. For the conjunctive form of

transition conditions ¬d

∧ d

, there is at least an

assignment of value false to d

and value true to d

which make the conjunctive form hold. Therefore,

transition t

is enabled and then ﬁred in the current

marking (p

Deﬁnition 10 (Reachable marking). Let W =

(P ,V,C, G,W, TV) be a WTC-net, a marking (M, σ)

with σ=t

. . .t

is reachable iff a sequence of reach-

able markings M

. . . M

exists such that (i, ε)

→

)

→ (M

)

→ . . .

n−1

→ (M

n−1

. . .t

n−1

)

→

. . .t

) with M

= M.

With the behavioural semantics of a WTC-net sys-

tem, we propose an extended coverability graph Al-

gorithm based on that Finkel has proposed in (Finkel,

1991). The constructed graph of Figure 1 is shown

in Figure 2 [An aside: any node with gray cycle is a

dead node, node 2 (p

) is the start state of the ﬁrst

cyclic execution t

, node 4 and node 9 labeled with

, {(t

, c

)}) are the start state of the second round

and third round of cyclic execution t

respectively,

Thus, the repeating of the cyclic executions is termi-

nated in the start state of the third round by merging

the node 9 to node 4 with the directed dotted arc].

2.3 Infeasible Trace of WTC-net

In this section, we will describe formally the seman-

tics of the infeasible traces of WTC-nets.

Deﬁnition 11 (Infeasible Trace). Let W =

(P ,V,C, G,W, TV) be a WTC-net, (M, σ) be a

marking of W , t be a transition with guard function

G(t), σ = t

...t

is the executable preﬁx of transition

t as well as trace σ·t is infeasible, iif:

i. M[t >, and

ii. there is an environment e : var ∪ ran(ψ) ֌ Val

such that for all 1 ≤ i ≤ |σ|,

holds

(ρ

∅, {(t, 0) | t∈ T }

(σ,true), e, TV), and

¬(V

holds

(ρ

∅, {(t, 0) | t∈T}

(σ.t, true), e, TV)).

Deﬁnition 12 (Correlation between transition condi-

tions). Given two transition conditions c

and c

as-

signed to guard function of t

and t

respectively. They

are correlated, iif:

(1) c

and c

reference common condition variables,

i.e, they have common condition variable set V

, v

, ..., v

(2) there is a trace from t

to t

such that at least one

variable in V

isn’t written.

Subsequently, we propose a backward search

algorithm on the generated coverability graph to

search the shortest infeasible trace [An aside: in

view of the limitation of space, for full details about

the algorithms we proposed the readers are referred

to http://laudms.thss.tsinghua.edu.cn/trac/Test/wiki/

chengguo/ICEIS2012.pdf].

Figure 3 shows the result of this detecting algo-

rithm. The set of infeasible traces t

)

∗

is caused by correlation relationship between transi-

tion condition c

on t

and transition condition c

as well t

)

∗

caused by correlation re-

lationship between transition condition c

on t

and

transition condition c

on t

3 EXPERIMENTS

We implemented the proposed approach for detecting

the infeasible traces of WTC-nets. We made use of a

well-known, open-source process analysis framework

(ProM) (van der Aalst et al., 2009) and developed our

tool as a ProM 6 analysis plug-in

. Figure 4 shows

the returned result of detecting the infeasible traces in

Figure 1.

Subsequently, we illustrate the applicability of our

approach to real process models by carrying out ex-

periments that are based on process models and data

information related with transition conditions found

in the TiPLM system

. These 29 collected real pro-

cess models are divided into 4 types: engineering de-

sign and review (DR), process engineeringand chang-

ing (PC), release management (RM), and applica-

tion management (AM). Firstly, we transformed the

TiPLM workﬂow models and the extracted data in-

formation from TiPLM database into WTC-net mod-

els. We then used the implemented tool to detect the

infeasible traces.

The ProM framework can be downloaded from

http://www.processmining.org/

TiPLM is a product life-cycle management solu-

tion, which is developed by THsoft InfoTech company

(http://www.thit.com.cn) and widely used in Mainland

China (well over 100 companies in the manufacturing in-

dustry in China adopted the TiPLM system).

DetectingInfeasibleTracesinProcessModels

215

(i, ε)

, t

)

, t

)

, t

)

, t

)

, t

)

, t

)

(o, t

)

, t

)

, t

)

(o,t

)

(o, t

)

(o,t

)

, t

)

(o, t

)

, t

)

(o,t

)

(o, t

)

(o,t

)

, t

)

, t

)

, t

)

,{(t

, c

)})

,{(t

, c

)})

Figure 2: The coverability graph of the WTC-net in Figure 1.

(i, ε)

, t

)

, t

)

, t

)

, t

)

, t

)

, t

)

, t

)

, t

)

, t

)

, t

)

, t

)

,{(t

, c

)})

Infeasible trace set:

)*t

Shortest infeasible trace

]

w: d

]

Projecting of Shortest infeasible trace in process model

,{(t

, c

)})

(a) Sample 1 for shortest infeasible traces

(i, ε)

, t

)

, t

)

, t

)

, t

)

, t

)

, t

)

, t

)

, t

)

]

w: d

]

Infeasible trace set:

)*t

Shortest infeasible trace

Projecting of Shortest infeasible trace in process model

,{(t

, c

)})

,{(t

, c

)})

(b) Sample 2 for shortest infeasible traces

Figure 3: Backwards detecting shortest infeasible trace.

Figure 4: The screenshot of the detecting result of the shortest infeasible traces.

Table 2 shows that there are 8 (27.6%) process

models among the 29 transformed WTC-net models.

We compared the detection results with other mea-

sures including manual analysis. It turned out that

our approach was always able to correctly detect the

correlation relationship of the process deﬁnitions. All

ICEIS2012-14thInternationalConferenceonEnterpriseInformationSystems

216

Table 2: The detecting result of infeasible traces for real process models

PM DR-1 DR-2 DR-3 DR-4 DR-5 DR-6 DR-7 DR-8 DR-9 DR-10

SIT

0 2 26 0 0 0 1 0 0 0

PM DR-11 PC-1 RM-1 RM-2 RM-3 RM-4 RM-5 RM-6 RM-7 RM-8

SIT

11 0 0 2 1 0 0 0 0 0

PM RM-9 RM-10 RM-11 RM-12 RM-13 AM-1 AM-2 AM-3 AM-4

SIT

0 0 0 1 0 0 1 0 0

∗

PM describes process model, SIT

denotes the number of the set of infeasible traces possessing the same shortest infeasible traces

examples for experiments can be downloaded from

http://laudms.thss.tsinghua.edu.cn/trac/Test/wiki/che-

ngguo/Test%20Data.zip.

4 RELATED WORK

In recent years, there are well-developed formalisms

for workﬂow modeling taking data perspective into

account based on WF-nets proposed in (van der Aalst,

1998).

In (Fan et al., 2007), a model called Dual Work-

ﬂow Nets (DWF-nets) was proposed, which can ex-

plicitly model both the control ﬂow and the data ﬂow

as well as their interactions. WFD-nets was proposed

in (Trˇcka et al., 2009) to extend WF-nets with data el-

ements for soundness veriﬁcation. However, both of

DWF-nets and WFD-nets don’tconsider the effects of

concrete guard functions as well as their propagation

explicitly.

For us, WTC-net is proposed for studying work-

ﬂow nets where routing may be determined by transi-

tion conditions. Further, the shortest infeasible trace

is detected based on the correlation between transi-

tions while the works in (Fan et al., 2007) and (Trˇcka

et al., 2009) focusing on the correctness of the auto

execution of workﬂow models.

5 CONCLUSIONS

In this paper, we have deﬁned workﬂow net with tran-

sition conditions WTC-net and its behavior semantics

with the inﬂuence of transition condition in detail. In

addition, we have presented an approach to detect in-

feasible trace and a tool has been implemented based

on the approach.

In the future work, we will consider how to verify

process model considering with transition condition

in quantity.

ACKNOWLEDGEMENTS

This paper is supported by the 863 High-Tech De-

velopment Program of China (No. 2009AA043401),

the National Science Foundation of China (No.

61003099, 61073005) and the National Sci-

ence and Technology Major Project, China (No.

2010ZX01042-002-002-01).

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