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Graphs, reactive systems and mobile ambients. Supervisor: F. Gadducci. Giacoma Valentina Monreale. Sound and complete w.r.t. the structural congruence of MAs. Graphical encoding for MAs. Syntax: P:= 0 , n[P], M.P, ( n)P, P 1 |P 2 M:= in n, out n, open n. ambient name. process.

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Graphs, reactive systems and mobile ambients

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## Graphs, reactive systems and mobile ambients

Supervisor:

Giacoma Valentina Monreale

Sound and complete w.r.t. the structural congruence of MAs

### Graphical encoding for MAs

Syntax: P:= 0, n[P], M.P, ( n)P, P1|P2 M:= in n, out n, open n

ambient name

process

activation point

ambb

cap

go

n[P]

cap n.P

(n)(n[in m.0]|m[out m.0])

go

a

ambb

inb

m

p

ambb

out

### Graph trasformation systems for MAs

Graphs trasformation rules

Reduction Semantics

n[P]|open n.Q P|Q

n[in m.P|Q]|m[R] m[n[P|Q]|R]

m[n[out m.P|Q]|R] n[P|Q]|m[R]

### LTS on graphs by the BC technique

We derive a LTS on graphs by applying the borrowed context technique, which is an instance of the theory of reactive systems

JFK

-|m[X]

G J

H

K

(n)n[in m.0]

(n)m[n[0]|X]

### LTS for MAs

The bisimilarity on the distilled LTS is too strict

We propose notions of strong and weak barbed saturated semantics for LTS synthesized using the theory of reactive systems

### (Weak) Barbed Semi-Saturated Bisimilarity

Barbs are predicates over the states of a system: Po if P satisfies o

Weak barbs: Po if P P’ and P’o

*

• Definition. A symmetric relation R is a

• bisimulationif whenever P R Q then

• ∀ C[−], if C[P]↓o then C[Q] o;

• if P P′ then C[Q] Q′ and P′ R Q′.

barbed semi-saturated

weak barbed semi-saturated

C[-]

*

• Weak barbed semi-saturated bisimilarity∼WBSS is the largest weak barbed semi-saturated bisimulation.

Barbed semi-saturated bisimilarity∼BSS is the largest barbed semi-saturated bisimulation.

(Weak) Barbed saturated bisimilarity for MAs coincides with (weak) reduction barbed congruence