Loading in 5 sec....

Mapping Fusion and Synchronized Hyperedge Replacement into Logic ProgrammingPowerPoint Presentation

Mapping Fusion and Synchronized Hyperedge Replacement into Logic Programming

Download Presentation

Mapping Fusion and Synchronized Hyperedge Replacement into Logic Programming

Loading in 2 Seconds...

- 59 Views
- Uploaded on
- Presentation posted in: General

Mapping Fusion and Synchronized Hyperedge Replacement into Logic Programming

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Dagstuhl Seminar #05081, 20-25 February 2005

Mapping Fusion and Synchronized Hyperedge Replacement into Logic Programming

Ivan Lanese

Dipartimento di Informatica

Università di Pisa

joint work with

Ugo Montanari

To be published on a special issue of Theory and Practice of Logic Programming

- Lot of background
- Fusion Calculus
- Synchronized Hyperedge Replacement
- Logic programming

- From Fusion Calculus to Hoare SHR
- From Hoare SHR to logic programming
- Conclusions

- Many models proposed for global computing systems
- Each model has its strengths and its weaknesses
- Comparing different models
- To understand the relationships among them
- To devise new (hybrid) models

- Cannot analyze all the models, naturally…

- Lot of background
- Fusion Calculus
- Synchronized Hyperedge Replacement
- Logic programming

- From Fusion Calculus to Hoare SHR
- From Hoare SHR to logic programming
- Conclusions

- Process calculus that is an evolution of -calculus
- Simpler and more symmetric but also more expressive
- Introduces fusions of names

- Agents:
S::=i i.Pi

P::=0 | S | P1|P2 | (x)P | rec X. P | X

Processes are agents up to a standard structural

congruence

- Follows the approach of graph transformation
- (Hyper)edges are systems connected through common nodes
- Productions describe the evolution of single edges
- Local effect, easy to implement

- Productions are synchronized via constraintson nodes
- Global constraint solving algorithm to find allowed transitions
- Productions applied indipendently
- Allows to define complex transformations

- A production describes how the hyperedge L is transformed into the graph R

L

R

H

H

3

3

4

4

2

2

1

1

L

R

H

3

3

4

4

2

2

1

1

1

1

2

2

3

3

R’

L’

- A production describes how the hyperedge L is transformed into the graph R

H

Many concurrent rewritings are allowed

- Productions associate actions to nodes
- A transition is allowed iff thesynchronization constraints imposed on actions are satisfied
- Many synchronization models are possible (Hoare, Milner, ...)

a

a

a

a

B1

A1

3

3

B2

A2

- Hoare synchronization: all the edges must perform the same action

- Milner synchronization:pairs of edges do complementary actions

- We use name mobility

- Actions carry tuples of references to nodes (new or already existent)
- References associated to synchronized actions are matched and corresponding nodes are merged

a<x>

a<x>

a<y>

B1

A1

a<y>

(x)

(y)

x=y

B2

A2

Very quickly…

- Syntax
- Semantics

- Lot of background
- Fusion Calculus
- Synchronized Hyperedge Replacement
- Logic programming

- From Fusion Calculus to Hoare SHR
- From Hoare SHR to logic programming
- Conclusions

- We separate the topological structure (graph) from the behaviour (productions)
- We give a visual representation to processes
- Processes translated into graphs
- Sequential processes become hyperedges
- Names become structures called amoeboids

- Our approach deals only with closed processes

- We take agents in standard form
- restrictions with inside parallel composition of sequential agents

- We transform it into a linear agent + substitution

- We translate the process into a graph
- Each linear agent becomes an edge labelled with a copy of the agent with standard names
- Q(x1,y1,z1) becomes an edge labelled by Q(x1,x2,x3) attached to x1,y1,z1

- σ transformed into amoeboids
- Each amoeboid connects a group of names merged by σ

- Each linear agent becomes an edge labelled with a copy of the agent with standard names

x1x2x3.R(x4,x5)

x

x1

z1

Q(x1,x2,x3)

y1

z

x2

x3

y

y2

z2

z3

u2

u1

w1

u3

x1x2x3.S(x4,x5)

u

w2

w

- We have actions for input and output prefixes
- Productions for process edges
- Correspond to executions of prefixes of normalized linear agents
- Prefixes modeled by corresponding SHR actions
- RHS contains the translation of the resulting sequential process
- Fusions implemented by connecting nodes via amoeboids

x2

x3

x1x2x3.R(x4,x5)

y2

R(x1,x2)

u2

u1

x2

x3

y2

u2

u1

out2x2y2

in x

out y

P

Q

y

x

- Amoeboids must allow two complementary actions on the interface and create new amoeboids connecting corresponding names
- Connected amoeboids are merged

P

Q

=

- Amoeboids implemented as networks of edges with a particular structure
- composed essentially by edges that act as routers
- each internal node is shared by two edges
- some technical conditions

- Satisfy the desired properties but…
- interleaving must be imposed from the outside
- produce some garbage (disconnected from the system)

- Reductions of fusion processes correspond to (interleaving) HSHR transitions
- up to garbage
- up to equivalence of amoeboids that does not change the behaviour

- The correspondence can be extended to computations

x1x2x3.R(x4,x5)

x

Q(x1,x2,x3)

z

y

out x2 y2

x1x2x3.S(x4,x5)

u

in z2 w1

w

x

Q(x1,x2,x3)

z

y

R(x1,x2)

S(x1,x2)

u

w

FusionHoare SHR

Closed processGraph

Sequential processHyperedge

NameAmoeboid

PrefixAction

Prefix executionProduction

Reduction Transition

- Lot of background
- Fusion Calculus
- Synchronized Hyperedge Replacement
- Logic programming

- From Fusion Calculus to Hoare SHR
- From Hoare SHR to logic programming
- Conclusions

- Useful for implementation purposes
- Logic programming as goal rewriting engine
- Very similar syntax (with the textual representation for HSHR)
- Logic programming allows for many execution strategies and data structures we need some restrictions
- limited function nesting
- synchronized execution

- We define Synchronized Logic Programming (SLP)

- A transactional version of logic programming (in the zero-safe nets style)
- Safe states are goals without function symbols (goal-graphs)
- Transactions are sequences of SLD steps
- During a transaction each atom can be rewritten at most once
- Transactions begin and end in safe states
- Transactions are called big-steps
- A computation is a sequence of big-steps

- Clauses with syntactic restrictions
- bodies are goal-graphs
- heads are A(t1,…,tn) where ti is either a variable or a single function symbol applied to variables

- Graphs translated to goal-graphs
- edges modeled by predicates applied to the attachment nodes

- Productions are synchronized clauses
- Transitions are matched by big-steps
- Actions are implemented by function symbols
- the constraint that all function symbols have to be removed corresponds to the condition for Hoare synchronization
- names are the arguments of the function symbol
- we choose the first one to represent the new name for the node where the interaction is performed (needed since substitutions are idempotent)
- fusions performed by unification

- Correspondence between HSHR transitions and big-steps
- An injective (at each step) substitution keeps track of the correspondence between HSHR nodes and logic programming variables

y

y

C

C

x

z

C

x

C(x,y)←C(x,z),C(z,y)

r <w>

y

y

C(r(x,w),r(y,w))←S(y,w)

C

S

(w)

x

x

r <w>

S

S

S

C

C

C

x

C

S

C

C

C

C

C

C

S

S

S

C

C

C

x

C

S

C

C

C

C

C

C

Hoare SHR SLP

GraphGoal

HyperedgeAtom

NodeVariable

Parallel comp.AND comp.

ActionFunction sym.

ProductionClause

TransitionBig-step

- Lot of background
- Fusion Calculus
- Synchronized Hyperedge Replacement
- Logic programming

- From Fusion Calculus to Hoare SHR
- From Hoare SHR to logic programming
- Conclusions

- Many relations among the three models
- similar underlying structure (e.g. parallel composition)
- name generations ability
- fusions

- Distinctive features
- Fusion: same structure for system and elementary actions, interleaving semantics, Milner synchronization, restriction
- HSHR: distributed parallel computations, Hoare synchronization, synchronous execution
- SLP: Hoare synchronization, asynchronous execution engine

- Analyzing different name-handling mechanisms
- In π calculus bound names are guarenteed distinct
- Useful for analyzing protocols (nonces, key generation)

- Hybrid models
- Different synchronizations for Fusion or logic programming
- Process calculi with unification (of terms)
- Logic programming with restriction

- Logic programming for implementation purposes
- For HSHR systems
- For Fusion Calculus

Thanks

Questions?

w

z

Ring Example

x,y,w,z C(x,w) | C(w,y) | C (y,z) | C(z,x)

- Transitions

G1 ,,I G2

: (A x N* ) (x, a , y) if (x) = (a , y)

is the set of new names that are used in synchronization

= {z | x. (x) = (a , y), z , z set(y)}

I contains new internal names

- Computations

1

2

n

0 G0 1 G1 … n Gn

- Productions

x1,…,xn L(x1,…,xn) x1,…,xn , , IG

Names can be merged (and new names can be added)

Identity productions are always available

- Transitions
are generated from the productions by applying the transition rules

for the chosen synchronization model

e <>

y

y

C

C

x

z

e <>

C

x

(x,ε,<>)(y,ε,<>)

x, y

C(x,y)

x, y, z

.C(x,z) | C(z,y)

r <w>

y

y

C

S

(w)

x

x

r <w>

,

(x,r,<w>)(y,r,<w>)

x, y

x, y

S(w,y)

C(x,y)

Process: agent up to the following laws:

- | and + are associative, commutative and with 0 as unit
- -conversion
- (x)0 = 0, (x)(y)P=(y)(x) P
- P|(x)Q=(x)(P|Q) if x not free in P
- rec X.P=P[rec X.P/X]