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Formal requirement language and its applications

A.LetichevskyGlushkov Institute of Cybernetics

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Formal requirement language BPSL

(Basic Protocol Specification Language)is an insertion modeling language

used for formal representing requirementsin distributed concurrent systems design

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Historical prerequisitesof insertion modeling

А В

finite automata

Infinite registers with periodically defined transformations

Computer model Glushkov 1961-1965

Theory of descrete processors70-е

Joint software and hardware design

Theory of descrete processors70-е

Joint software and hardware design

Models of macroconveyer computations

80-е

Insertion programming and

modeling2000 - ...

cooperation with Motorola Theory of interaction of

agents and environemnts90-е

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nenvironment

environment

agents

Insertion function

4

А В

Finiteautomata

Infinite registers withperiodically definedtransformations

BiAyxxFx jiiiii ),,...,,(21

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80-еMacroconveyercomputations overdata structures

Active agents passive

environment

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Active environment

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nenvironment

environment

agents

Insertionfunction

Possesses behavior which is changed when new agents are inserted into it

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Insertion modelingTechnology of constructing and studying

of real systems models by representing them as compositions of interacting

agents and environments

FormalyAgents: labeled transition systems

Environments: attribute transition systemsComposition: continuous insertion function

characterizing the behavior of environment with agents inserted into it

A kind ofModel Driven Engineering

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Simple example: readers and writers

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environment( agent types:( reader: (

registered: Bool, access allowed: Bool

), writer: Nil ); attributes:( rec: symb, queue: list of symb ); safety condition: Forall(m:reader)( m.access allowed->m.registered ); initial condition:( Forall(m:reader)( ~(reader m.registered)& ~(reader m.access allowed) ) ));

Environment description

BPS = environment description +[agent behaviors] + basic protocols

Agent behaviors

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state reduction: rs(x)( reader init = register.(loop read; release), writer init = (loop write; release), loop x = (x;(loop x + Delta)))

incorrect state reduction: rs()( reader init = register state + read state + release state, register state = register. reader init, read state = read. reader init, release state = release. reader init, writer init = write state + writer release, write state = write. writer init, writer release = release. writer init)

Basic protocols: register and read

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reader m env

reader(m, register.s)&

~(reader m.registered)

reader(m, s)&

reader m.registered

register m

ok

register(m,s)

reader m env

reader(m, read.s)&

reader m.access allowed

reader(m, s)&

~(reader m.access allowed)

read m

rec

read(m,s)

Forall(m,s)

Release and write

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reader m env

reader(m, release.s)&

reader m.registered

reader(m, s)&

~(reader m.registered)

release m

ok

release(m,s)

writer m env

writer(m, write x.s)

writer(m, s)&

add_to_tail(queue,(m:x))

write(m:x)

ok

write(m,s,x)

Forall(m,s,x)

Update

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rec

update x

update(x,t)

(queue=t)&(rec=x)&

Forall(n:reader)(n.registered->

n.access allowed)

(queue=(x,t))&

Exist(n:reader)(n.registered)&

Forall(n:reader)(n.registered->

~(n.access allowed))

queueForall(x,t)

BPSL partially implemented in VRSenvironment description

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Types: Data types

simple: int, real, Bool, intervals, enumerated, symbolic (free terms), agent behaviors (process algebra), ADT

lists: list (m) of τ (simple)functional: (simple, arrays are considered as functional types)

Agent types: defined by the set of typed agent attributes

Environment attributes:used as functional symbols (simple= arity 0)

Agent attributes: typed namesInstances: (for MSC as processes in BPs)Axioms: formulas without attributes (ADT)Rewriting rule systems: equations as in APS (ADT and normal forms) Initial states: formula of basic language or concrete state

,...),( 21

Abstract representation of basic protocol

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Algebraic representation:

x – list of typed parameters, P – process, and are pre- and postconditions.

Preconditions:1-st order formula with the following literals:

State assumptions (like reader(m, release.s)) Linear inequalities for numericEqualities and disequalities for symbolicBoolean attribute expressions Uninterpreted predicates

Postconditions:1-st order formula as in precondition Assignments x:=y considered as statements x´=y Updating lists

))()()(( Forall xxPxx )(x )(x

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Semantics of BPSL

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Defined by the notion of implementation: Attributed transition system with validity relation s|=α ,…such that for each BP and its instantiation

(direct implementation)

(inverse implementation)

For each finite MSC C such that (permutability relation on actions and partially sequential composition of processes).Concrete implementations: interpretation of signature and initial states are fixed as well as deterministic transitions, validity is computed from attribute valuations. Abstract implementations: interpretation of signature and initial states are not fixed, validity is inferenced from the states labeling.

|,| ][][ ssss CB

))()()(( Forall xxPxx )(tPB

][][ CB

|),|( ][][ ssss CB

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Some new results on abstractions

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A class of concrete implementations Concr(P) is defined and proved to be direct and inverse implementations of consistent BPS P.

Two classes Adir(P) and Ainv(P) of direct and inverse abstract implementations has been defined and proved to be implementations of consistent BPS P.

Each abstract implementation is an abstraction of some concrete one.

There exist the most abstract implementation (is an abstraction of all concrete implementations).

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Tools forstatic and dynamic

requirements checking

The applications of BPSL

VRS Verification of Requirement

Specificationsa tool developed

for Motorola

Formalizing requirementsExperience in Telecommunications, telematics and other application domains

(projects for Motorola) Formal description of MPI library

(projects for Intel)

Generating tests from requirement specifications

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Static requirements checking

• Proving consistency and completeness

• Proving safety

• Computing invariantsPreconditions for BPs (with the same external actions) must not

intersect

Disjunction of preconditions is valid

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Symbolic trace generation

• Checking applicability of protocol– Satisfiability of current state and precondition

– Proving existential formula

• Computing predicate transformer– Proving predicate transformer formula

• Combining numeric and symbolic constraints

• Using data structures (arrays, lists etc.)

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Experience in application of VRS

Tens of application systems from the domains:Telecommunications

Embedded systemsReal time systems

Sizes of formal requirements:Southands of basic protocols Handreds of attributes

Handreds of errors found in documentationsSouthands of tests providing complete covering of requirements Transition from piloting to commercial use of VRS tools.

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Some new application domains

Parallel computations:Formalization of MPI libraryMethods of checking of correctness of parallel programs

using MPIInformation security:

Experiments on finding the possibility of attac on secure protocols of secret data exchange.

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