1 formal models for transactions: zero safe nets roberto bruni dipartimento di informatica...

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Formal Models for Transactions: Zero Safe Nets

Roberto BruniDipartimento di Informatica Università di Pisa

Models and Languages for Coordination and Orchestration

IMT- Institutions Markets Technologies - Alti Studi Lucca

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Roberto Bruni @ IMT Lucca 13 April 2005


InstitutionsMarketsTechnologies

IMT

Contents Orchestration with Petri Nets Transactions with Zero Safe Nets From BizTalk to Zero Safe Nets

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Why Extending Petri Nets P/T nets can naturally model

control flow data flow message passing

The basic P/T net model does not offer any synchronization between transitions (only token synchronization)

that would be useful for expressing transactions

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Why Zero-Safe Nets Zero-Safe Nets offers a basis for modeling

distributed transactions and workflows simple and natural extension of Petri nets based on a concept easily exportable to other

paradigms offering both refined / abstract views admit distributed interpreters / implementations

based on unfolding, no backtracking based on join-calculus

easy to combine with other net flavors (e.g. read arcs)

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The Idea Zero-Safe Nets are like P/T Petri nets but places

are partitioned in Stable places

ordinary places defining observable states Zero-Safe places (or just zero places)

idealized resources empty in all observable states temporarily used during transactions (coordinating

activities) Transactions as transition synchronizations

a computation from observable states to observable states via non-stable markings

transactions can end when all tokens in zero places have been consumed

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Rendez-Vous

send receive

The message can be sent

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Rendez-Vous

send receive

Sender is blocked until message is received

Frozen!

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Rendez-Vous

send receive

Ready to commit

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Rendez-Vous

send receive

Coordinated commit

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Nondeterministic Rendez-Vous

send

receive

receive

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Origin of the Name In classic Petri net Theory

A place a is n-safe if in any reachable marking it contains at most n tokens

A net is n-safe if all its places are such Thus a place / net is 0-safe if in any reachable

marking it is empty! Useless?

We write zero-safe, not 0-safe Zero places must be empty in any observable

marking

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From Free-Choice to Non-Deadlocking

turn turn

left leftright right

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turn turn


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turn turn


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turn turn


Success!

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turn turn


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turn turn


Deadlock!

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turn turn


Only successful choicesby design!

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No Reuse of Stable Tokens Before Commit

send receive

The message can be sent…

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No Reuse of Stable Tokens Before Commit

send receive

…but no-one can receive it!

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Multicasting

b

a

z

c

2

new

receive

send

reset copy

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Multicasting

b

a

z

c

2

new

receive

send

reset copy

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Multicasting

b

a

z

c

2

new

receive

send

reset copy

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Multicasting

b

a

z

c

2

new

receive

send

reset copy

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Multicasting

b

a

z

c

2

new

receive

send

reset copy

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Formal Definition A Zero-Safe net is

B=(S,T,pre,post,u0,Z) NB=(S,T,pre,post,u0) is the underlying P/T

Petri net ZS is the set of zero places

L=S-Z is the set of stable places u0L is the initial marking

Note: S = (LZ) LZ Markings can be represented as pairs (u,x)

uL

xZ

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Operational Semantics We can exploit the operational semantics (step

semantics) of the underlying P/T Petri net NB

uxNBvy

(u,x)B(v,y)[underlying steps]

(u,)B(v,)

uBv[commit]

(u,x)B(v,x’) (u’,x’)B(v’,y)

(uu’,x)B(vv’,y)[horizontal composition]

The key feature is horizontal composition• it acts as sequential composition on zero places• it acts as parallel composition on stable places

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Transactions as Transitions

The admissible behaviors of the net are those that can be committed Such concurrent transactions can be regarded as

atomic activities at the higher level of abstraction In general there can be several P/T Petri nets

N such that N B We should select an abstract net A(B) which

is an ordinary P/T Petri net its places are the stable places of B its transitions are the (minimal) transactions of B

not decomposable in parallel activities all other steps can be inferred

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Rendez-Vous

send receive

B A(B)

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turn turn


turn-L turn-R

B A(B)

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Collective or Individual? Different philosophies can yield different abstract

nets Define an algebra of computations

Careful axiomatization of horizontal composition * Select only those computations such that

goes from stable marking to stable marking If there exist , with = then either = or =

Computations are processes of NB Select only those processes that satisfy suitable conditions

connected – not decomposable in parallel active processes all and only minimal / maximal places stable full – no idle place

CTPh

ITPh

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Multicasting CTPh

b

a

c

new

1-1reset

2

2

1-2

3

3

1-n

n+1

n+1

… …

Infinitely many transitions!

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Multicasting ITPh

b

a

c

new

1-1reset

2

2

1-2

3

3

1-n

n+1

n+1

… … 1-n

n+1

n+1

…

Different copy policies are distinguished!Infinitely many transitions!

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Concurrent Copies

send copy

copy

copy

receive

receive

receive

receive

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Sequential Copies

send copy

copy

copy

receive

receive

receive

receive

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The ITPh “Monster”

B CTPh ITPh

2

2

n

n

… …

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FIFTH HOMEWORK Show that given any Zero Safe net B, we can

always find a corresponding Zero Safe net Bbase

that: Bbase yields the same abstract net as B and Bbase contains only transitions of the form

below:

fork

open join close drop

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Extensions of Zero-Safe Nets

Read arcs multiple concurrent reading of the same

token Data values

colored tokens / high level nets Dynamic net reconfiguration many others currently under

investigation

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References Zero-safe nets: comparing the collective

and individual token approaches (Information and Computation 156(1-2):46-89, 2000) R. Bruni, U. Montanari

Extending the zero-safe approach to colored, reconfigurable and dynamic nets (Advances in Petri Nets, LNCS 3098, pp. 321-336, 2002) R. Bruni, H. Melgratti, U. Montanari

1 formal models for transactions: zero safe nets roberto bruni dipartimento di informatica...

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