Compositional Process Model Synthesis based on Interface Patterns TMPA-2017 Roman A. Nesterov Irina A. Lomazova [email protected], [email protected] Laboratory of Process-Aware Information Systems National Research University Higher School of Economics (Moscow) March 3, 2017

Agenda 1. Introduction 2. Preliminaries • Petri nets and their properties 3. Related Work 4. Composing Petri nets via interfaces • General description • Composition patterns 5. Conclusion R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 2 / 25

Introduction Problem • Distributed systems with several interacting components – large-scale models • Coordination and verification problems – too many possible states to check Approach • Study a system compositionally – a system inherits component properties • Composition patterns for constructing system models – a library of patterns to obtain correct system models R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 3 / 25

Petri nets Structure A B B B A Petri net is a bipartite graph N = (P, T, F, m0, L), where: 1. P = {p1, p2, p3, ..., pn} 2. T = {t1, t2, t3, ..., tm}, P ∩ T = ∅ 3. F ⊆ (P × T) ∪ (T × P) 4. m0 ⊆ P 5. L : T → {A, τ} •t = {p ∈ P|(p, t) ∈ F}, t• = {p ∈ P|(t, p) ∈ F}, •t• = •t ∪ t• R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 4 / 25

Petri nets Behavior and correctness A B B B A occurred 1. A transition is enabled at m iff •t ∈ m and m ∩ t• = ∅ 2. A marking m is final iff ∀p ∈ m : p• = ∅ 3. A marking m is dead iff it enables no transitions (deadlock), except for a final one 4. A net N is correct iff: • There are no deadlocks • A final marking is reachable R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 5 / 25

Related work Composing Petri nets by merging places, transitions [Reisig, 2013] D E C p A B p D E C A B p N1 N2 Composition • Straightforward way to compose nets • Correctness of a composed net? R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 6 / 25

Related work Composing Petri nets by net morphisms [Pomello et al., 2007-1014] C D A B A B E F A1 A B E F A C D B N1 N2 Composition • Interacting nets are refinements of an abstract system model R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 7 / 25

Related work Algebra of web services [Hamadi et al., 2003] S1 S2 S1 S2 S1 S2 Sequencing Choice Concurrency Correct services • Web services are correct Petri nets • Input-output relations between interacting services R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 8 / 25

Motivating example Causality on inner actions of interacting Petri nets … B … … A … A B Components Interface A correct Petri net • Two components • Observable actions A, B • Correct behavior Problem How to compose nets to get: • correct composition; • property inheritance; • concurrency preservation? Solution To adjust approach based on morphisms to this case R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 9 / 25

Morphisms Definition Let Ni = (Pi, Ti, Fi, mi 0 ) for i = 1, 2 be two Petri nets, Xi = Pi ∪ Ti . The ω-morphism is a map φ : X1 → X2 such that: 1. φ(P1) = P2 , φ(m1 0 ) = m2 0 . 2. ∀t1 ∈ T1 : φ(t1) ∈ T2 ⇒ φ(•t1) = •φ(t1) and φ(t1 •) = φ(t1)•. 3. ∀t1 ∈ T1 : φ(t1) ∈ P2 ⇒ φ(•t1 •) = {φ(t1)}. A A’ A B B’ R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 10 / 25

Composing Petri nets via morphisms Step 1. Constructing canonical representations NC is a canonical representation with respect to an interface A A B A A B B A A B A A B B N Interface NC R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 11 / 25

Composing Petri nets via morphisms Step 2. Defining morphisms and merging nets C D A B A B E F A1 A B E F A C D B N1 N2 Composition R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 12 / 25

Composing Petri nets via morphisms Preservation of properties How properties are preserved? Let N1 and N2 be two Petri nets representing components, and N be their composition obtained via the interface Petri net NI and ω-morphisms as described above. 1. The Petri net N is deadlock-free, if N1 , N2 and NI are deadlock-free. 2. The Petri net N terminates properly, if N1 , N2 and NI terminates properly. A composed net is correct iff component nets are correct R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 13 / 25

Compositional patterns General idea Compositional pattern is a ready-to-use instrument for modelling and studying distributed systems with several interacting components: • Patterns are developed for typical workflows • Pattern correctness is justified via net morphism usage • Pattens can be applied without theoretical knowledge R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 14 / 25

Pattern 1: Simple causality Problem statement … B … … A … A B Components Interface A B Extended interface Termination Start A correct Petri net • Extended interface is weakly bisimilar to the original one • Preservation of concurrency R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 15 / 25

Pattern 1: Simple causality Primary composition result N1(S1) A N1(S2) B N2(S1) B N2(S2) A A B N1(S1) A N2(S1) B N1(S2) N2(S2) Morphisms Composition N1 N2 To be removed R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 16 / 25

Pattern 1: Simple causality Reduced composition result N1(S1) A N1(S2) B N2(S1) B N2(S2) A A B N1(S1) A N2(S1) B N1(S2) N2(S2) Morphisms Composition N1 N2 R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 17 / 25

Pattern 2: Extended causality Problem statement N1(S3) A N1(S4) N1(S2) N1(S1) A N2(S3) B N2(S4) N2(S2) N2(S1) A A B Components Interface A B A A Extended interface N1 N2 Termination Start R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 18 / 25

Pattern 2: Extended causality Composition result and implications N1(S3) A N1(S4) N1(S2) N1(S1) A N2(S3) B N2(S4) N2(S2) N2(S1) A Result • Introducing additional controlling places • Clearly identified behavior of components • Component properties are inherited by construction R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 19 / 25

Pattern 3: Conditional causality Problem statement N1(S3) N1(S2) N1(S1) A B N1(S5) N1(S4) N2(S1) C N2(S2) A B C C Components Interface N1 N2 Problem 2 copies of C will not allow to define morphisms as surjective maps Solution Reconstruction of the interface net R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 20 / 25

Pattern 3: Conditional causality Interface modification A C A C 2 1 B 3 C 4 Construction idea 1. Restrict execution of C 2. Remember execution of A 3. Restrict execution of B 4. Forbid execution of B when A occurs R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 21 / 25

Pattern 3: Conditional causality Composition result and implications N1(S1) A A N1(S2) N1(S3) N2(S1) A B C N2(S2) N1(S4) C N1(S5) To sum up... Morphisms help organize connection of inner actions of components immediately by construction R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 22 / 25

Conclusion • Compositional approach to modeling distributed systems • Component relations can be defined on inner actions • Patterns for composition (causality and its generalizations) Future research directions • Coverage of over relations (e.g., choice) • Combination of patterns • Relations on several actions R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 23 / 25

References 1. Reisig, W.: Understanding Petri nets. Springer-Verlag Berlin Heidelberg (2013) 2. Bernardinello, L., Mangioni, E., Pomello, L.: Composition of elementary net systems based on morphisms. CEUR Workshop Proceedings 853, 87–101 (2012) 3. Bernardinello, L., Monticelli, E., Pomello, L.: On Preserving Structural and Behavioural Properties by Composing Net Systems on Interfaces. Fundamenta Informaticae 80(1-3), 31–47 (2007) 4. Pomello, L., Rozenberg, G., Simone, C.: A survey of equivalence notions for net based systems. Advances in Petri Nets 1992 pp. 410–472 (1992) 5. Hamadi, R., Benatallah, B.: A Petri net-based model for web service composition. Proceedings of the 14th Australasian Database Conference 17, 191–200 (2003) 6. Murata, T.: Petri Nets: Properties, Analysis and Applications. Proceedings of the IEEE 77(4), 541–580 (1989) R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 24 / 25

Thank you for your attention! Compositional Process Model Synthesis based on Interface Patterns Roman A. Nesterov Irina A. Lomazova [email protected], [email protected] Laboratory of Process-Aware Information Systems National Research University Higher School of Economics (Moscow) March 3, 2017 R. Nesterov, I. Lomazova Higher School of Economics March 3, 2017 25 / 25