MAKING THE UNOBSERVABLE, UNOBSERVABLE.

Transcription

1 MAKING THE UNOBSERVABLE, UNOBSERVABLE. 3 PAPERS FROM THE LAST 365 DAYS AVAILABLE TO READ NOW ON YOUR COMPUTER PAWEL SOBOCINSKI AND JULIAN RATHKE GO TO

2 Plan of the talk Introduction & background Full asynchrony Asynchrony & Synchrony

3 Plotkin SOS (1981) A point to watch is to make a distinction between internal and external behaviour... It is a matter of experience to choose the right definition of external behaviour... Indeed on occasion one must turn the problem around and look for a transition system which makes it possible to obtain an expected notion of behaviour. internal = reduction (execution) ts expected notion = reduction congruence external = lts expected: bisimilarity = reduction congruence

4 RPOs Passing from an internal description to an external description Labels are smallest contexts which allow reduction

5 What s wrong with RPOs? 1. they often give wrong equivalences eg. asynchrony 2. labels are derived globally - no compositional, inductive presentation ie, no SOS

6 Our work We have concentrated on giving SOS descriptions of RPO-like LTSs Technically, this meant splitting derivation process into process contribution and context contribution using a metasyntax based on the simply typed lambda calculus Pi - Deconstructing behavioural theories of mobility. TCS 08. To appear. Ambients - Deriving structural labelled transitions for mobile ambients. Concur 08. To appear.

7 What s wrong with RPOs? 1. they often give wrong equivalences eg. asynchrony Goal of this talk - study this problem with aid of simple examples 2. labels are derived globally - no compositional, inductive presentation ie, no SOS

8 Plan of the talk Introduction & background Full asynchrony Asynchrony & Synchrony

9 Full asynchrony P ::= 0 a! a? P Q τ soup of interacting processes τ 0, a! a? 0 closed under parallel

10 Observation Observer can: introduce new ingredients into the soup measure change in heat Reduction precongruence: largest reduction simulation congruence Reduction congruence: largest reduction bisimulation congruence

11 Experiment 1 - Tau labelled transition = log of experiment tau experiment = experimenter observes heat without adding anything (Tau) P τ P (Tau) τ τ 0 P Q τ P Q

12 Experiment 2 - Input input experiment = experimenter observes heat a! after adding an output ( ) a? a? 0 (In) P a? P P Q a? P Q (In)

13 Experiment 3 - Output output experiment = experimenter observes heat a? after adding an input ( ) a! a! 0 (Out) P a! P P Q a! P Q (Out)

14 Another tauexperiment P a? P Q a! Q (Comm) P Q τ P Q

15 The LTS Sets of SOS Φ rules define idempotent monotonic functions on relations (lfp) Φ : P(P L P ) P(P L P ) Φ def = {(Tau), (Tau), (In), (In), (Out), (Out), (Comm)} Context Lemma C def = Φ( ) χ a! = a? χ a? = a! χ τ =0 P α P P χ α P

16 Soundness simulation reduction precongruence bisimulation reduction congruence Proof: show that tau-labelled transitions agree with reductions and that (bi) simulation is a (pre)congruence the last step follows from the construction

17 Experiment mismatch P 1 def = a? a! P 2 def = τ P 1 P 2 but P 1 C P 2 What has gone wrong? no account of unsuccessful experiments

18 Completing the LTS P τ P (InHT) P a? P a! P τ P (OutHT) P a! P a? Ψ def = {(InHT), (OutHT)} HT def = ΨC This completed LTS is sound and complete.

19 Plan of the talk Introduction & background Full asynchrony Asynchrony & Synchrony

20 Asynchrony P ::= 0 a! a?p P Q τp P ::= 0 a!p a?p P Q τp

21 Asynchronous experiments a?p a? P (In) a! a! R R (Out) P a! R P P Q a! R P Q (Out) P a? P Q a! 0 Q (Comm) P Q τ P Q

22 LTS Φ def = {(Tau), (Tau), (In), (In), (Out), (Out), (Comm)} C a def = Φ a ( ) context lemma soundness but... P 1 def = a?a! P 2 def = τ P 1 P 2 P 1 C P 2

23 Completing the LTS P τ P (InHT) P a? P a! P P τ P (OutHT) a! R P a?r Ψ def = {(InHT), (OutHT)} HT a def = ΨC a This completed LTS is sound and complete.

24 Refining Theorem - Outputs are observable: a! Q R R = a! R P τ P (InHT) P a? P a! P P τ P (OutHT) a! R P a?r

25 In general Making the unobservable, unobservable. ICE 08. To appear. in the paper we also consider the synchronous variant throwing in all the HT rules results in completeness for free one obtains better LTSs by only adding the necessary rules better = smaller bisimulations, more power