1. 1 Ivan Lanese Computer Science Department University of Bologna Italy Concurrent and located synchronizations in π-calculus

2. Roadmap l Process calculi l The standard semantics of π-calculus l A new located semantics l A new concurrent semantics l Conclusions

3. Roadmap l Process calculi l The standard semantics of π-calculus l A new located semantics l A new concurrent semantics l Conclusions

4. Process calculi l Behavioral models of concurrent interacting systems l Useful to analyze the properties of systems before building them –System satisfies some properties –Equivalence of different implementations –Correctness of optimizations l Systems modeled as terms in a suitable algebra –Constants for basic behaviours –Operators of composition (parallel composition, declaration of a resource, …)

5. Operational semantics l Allows to describe system behaviour l Two styles: reduction semantics and labelled semantics l Reduction semantics –Describes the evolution of a closed system –Easy to use and understand –Rules of the form l Labelled semantics –Describes the interactions between the system and the environment –Useful to describe open systems and analyze properties –Rules of the form P 1 ® ¡ ! P 2 P 1 ! P 2

6. Bisimilarity ≈ l Equivalence relation –Abstracts from internal details –Equates systems indistinguishable from the outside –Built on top of a reduction or a labelled semantics l Two processes are bisimilar if one can simulate the other (do the same actions going to bisimilar processes) and vice versa –Using reductions requires also context closure –More distinguishing than trace equivalence l Bisimilarity is compositional if preserved by contexts –Known as “bisimilarity is a congruence” property –Allows to substitute bisimilar processes without changing the behaviour (e.g., optimization) ≈ / aa bcbc a

7. Which calculus? l Different process calculi have been proposed, focused on different aspects (locations, cryptography, wireless communication, …) l We choose the π-calculus l Apt to model distributed mobile systems in an easy way l Used both in academia and industry –Basis for BPEL l Easy to extend to deal with different features (spi, dPi, stochastic pi, …)

8. Roadmap l Process calculi l The standard semantics of π-calculus l A new located semantics l A new concurrent semantics l Conclusions

9. π-calculus syntax l Names a,b,x,… represent communication channels l Channel names are the only data l Enough to encode booleans, integers, …

10. π-calculus reductions ≡ is an equivalence relation stating basic properties (e.g., parallel composition is associative and commutative)

11. Example ºnan : P [ n ] a ( x ) : b x : Q b ( x ) : R [ x ] a b

12. b ( x ) : R [ x ] b b n : Q P [ n ] n

13. P [ n ] n Q R [ n ]

14. π-calculus labelled semantics

15. Observations on the standard semantics l The semantics shows inputs, outputs, and synchronizations (τ) l All the synchronizations are equal –On a restricted or on a free channel –All free channels are equal l At each step exactly one action is performed –Concurrency indistinguishable from interleaving l We want to change these assumptions

16. The ideas of our approach l Many works considered locations and concurrency in π- calculus l Locations explicitly added: l::P l Concurrency using mappings to other formalisms (Petri nets, graphs, …) or complex algebraic structures (event structures, …) l We want to analyze what can be done without changing the framework –Standard π-calculus syntax –Direct semantics using standard labelled and reduction style –Trying to preserve the good properties of the standard framework

17. Roadmap l Process calculi l The standard semantics of π-calculus l A new located semantics l A new concurrent semantics l Conclusions

18. Located synchronizations l We want to see where a synchronization is performed l Different channels can have different properties –Accounting –Security policies –…–…

19. π-calculus located reductions l We need labels also for reductions l Labels show which (free) channel is used

20. Properties of the located semantics l Can be expressed also using the labelled semantics –Label aτ for a synchronization on free channel a –Label τ for a synchronization on a hidden channel l Full correspondance between reduction and labelled semantics –Reductions correspond to labelled synchronizations –They induce the same bisimilarity »Closure under substitutions needed for labelled semantics

21. Located bisimilarity l Located bisimilarity refines standard one a j a ¼ / L º b ( a + b )j( a + b ) a j a ¼ S º b ( a + b )j( a + b ) but l This allows to observe which channels are used l For instance we can distinguish between communication on a local network (free, safe) from communication via Internet (under accounting, unsafe)

22. Roadmap l Process calculi l The standard semantics of π-calculus l A new located semantics l A new concurrent semantics l Conclusions

23. Concurrent synchronizations l We want to see which actions can be performed concurrently l Actions can be executed concurrently provided that: –they are performed by different sequential processes –they are executed on different channels l One concurrent transition corresponds to one or more located transitions

24. π-calculus concurrent reductions l Labels contain the set of used channels

25. Properties of the concurrent semantics l Can be expressed also using the labelled semantics –Labels are (essentially) multisets of located labels l Full correspondance between reduction and labelled semantics –Reductions correspond to labelled synchronizations –They induce the same bisimilarity

26. Concurrent bisimilarity l Concurrent bisimilarity refines the located one but l This allows to distinguish concurrency from nondeterminism l Actions on the same channel are sequentialized a j b ¼ L a : b + b : aa j b ¼ / C a : b + b : a a j a ¼ C a : a

27. Compositionality l Concurrent bisimilarity is a congruence –This allows compositional reasoning about system behaviour –Bisimilar subcomponents can be substituted one for the other l This property does not hold for standard or located semantics –Standard and located bisimilarity not preserved by contexts that perform substitutions a j b ¼ L a : b + b : a but b j b ¼ / L b : b + b : b

28. Roadmap l Process calculi l The standard semantics of π-calculus l A new located semantics l A new concurrent semantics l Conclusions

29. Conclusions l Two new semantics for π-calculus highlighting –where synchronizations are performed –which synchronizations can be performed concurrently l The semantics capture these behaviours –More expressive power l Many good properties of standard semantics are preserved by the extensions –Correspondance between reduction and labelled semantics –Bisimilarities refine standard one l Additional property: concurrent bisimilarity is compositional

30. Future work l Further analysis on the new semantics –Weak semantics (first results in the paper) –Analysis techniques –Applications l Looking for semantics in the same style for other calculi l Analysing the effects of more concurrency –What happens if many actions are allowed on the same channel?

31. End of talk