Safety-Critical Systems 4Formal Methods / Modelling

T 79.232

Formal Methods and Safety-Critical Systems

Formal Methods are used in expressing requirements, design and analysis of a safety critical software and hardware.

There exists a need for using formal methods from writing requirements to verifying the system fullfilling those.

Formal Methods should be part of education of every computer scientist and software engineer, just as the appropriate branch of applied maths is a necessary part of the education of all other engineers. – John Rushby (FAA/NASA)

Method

Method (system engineering) consists of:

1) Underlying model of development (process)

2) Language (expressing formal specification)

3) Defined, ordered steps (phases)

4) Guidance for applying steps in a coherent manner (instructions)

Semi-formal Requirements/Specification

Requirements should be inambigious, complete, consistent and correct. - Natural language has the intepretation possibility. More accurate description needed.- Using pure mathematic notation – not always suitable for communication with domain expert. - Formalised Methods are used to tackle the requirement engineering. (Structured text, formalised English).

Domain Expert(s)

Text

Validation

Consistency

Validation

ModelInformal

Verification

Consistency

Implement.

Validation

Verification(Testing)

Consistency(another) Model

FormalVerification

Formal Methods/ Model orientatedThese languages involve the explicit specification of a state model - system‘s desired behaviour with abstract mathematical objects as sets, relations and fucntions.- VDM (Vienna Development Method) ISO standardisied.- Z-language - B-Method

Formal Methods/ Property orientated

Property orientated include axiomatic and algebraic methods.-Axiomatic use first order predicate logic to express pre/post conditions over abstract data types (Larch/ADA, Sternol)-Algebraic methods are based on multi and order sorted algebras and relate properties of the system to equations over entities of the algebra (Act One, Clear and varities of OBJ)

Formal Methods/Process orientated

Process algebras have been developed to meet the needs of concurrent systems.

-Theories behind Hoare‘s Communicating Sequential Processes (CSP) and Milner‘s Calculus of Communicating Systems (CCS). -Protocol specification language LOTOS is based on combination of Act One and CCS.

Language/Method selection criteria

Good expressiveness

Core of the language will seldom or never be modified after its initial development, it is important that the notation fulfils this criterion.

Established/accepted to use with Safety Critical Systems

Possibility of defining subset/coding rules to allow efficient automatic processing by tools.

Support for modular specifications – basic support is expected to be needed

Temporal expressiveness

Tool availability

Formal Methods/ Z-language

Z-language bases on first order predicate logic and set theory.

- The specification expressed in Z-notation is divived into smaller parts – schemas

- These schemas describe the statical and dynamical characteritics of the system:

static: possible states, invariantsdynamic: possible operations, pre/post states

- Z is an exellent tool for modelling data, state and operations

Simple example of Z notation

___BirthdayBook_______ known:PNAME birthday: NAME → DATE_____________________ known = dom birthday_____________________

___AddBirthday________∆BirthdayBookname?:NAMEdate?:DATE_____________________name? /€ knownbirthday’ =birthdayU{name? →date?}_____________________

___FindBirthday____________ΞBirthdayBookname?:NAMEdate!:DATE_________________________name?€ knowndate! = birthday(name?)_________________________

___Remind________________Ξ BirthdayBooktoday?:DATEcards!:PNAME_________________________cards!={n:known|birthday(n)=today?}_________________________

Formal Methods/ B-method

B is quite well-known. Although not as established as Z, B figures in some remarkable success stories of industrial applications of formal methods, eg by MATRA and (B Toolkit/UK) - B-method uses Abstract Machine Notation (AMN) for specification and implementation.

Formal Methods/ B-method

- Like Z, B is based on set theory and provides a rich set of operations.

- B includes facilities for modular specifications, although not as powerful as those of Z.

- The temporal expressiveness of B is poor. Only relations between a state and the next can be expressed.

Modeling Requirements

• Models needed for communicating with domain experts (simulation)

• Automatic verification (model checker, theorem proving)

Some Modeling Styles

Black Box

Glass Box

View point: versus

Functional Object-based

Decomposition: versus

Textual

Blabla

GFHP

Graphical

Representation: versus

Tools for Validation & Verification

•Tools for Validation– Static analysers derive implicit information about a model (or a program)

• Examples: KeY, VDMTools (IFAD), …– Simulators for executable specifications

• Examples: UML (Cassandra), MATLAB/Simulink, Statemate, …

•Tools for Verification– Model checkers for “brute force” enumeration of states

• Examples: Alloy, SATO, SMV/NuSMV, SPIN, Statemate, UPPAAL, Validas, …

– Theorem provers provide support for algebraic proofs of model properties• Examples: ACL2, Alloy, eCHECK (Prover Technologies), KIV, PVS

(SRI Inc.), TRIO-Matic, VSE II, …

Statemate modeling

• Based on Harel statecharts from 80‘s

• Functional decomposition

• Used years in aviation and car industry

• Mainly for simulating and validating functionality (Test cases)

• Model checker for verification

Functional Decomposition• Functional decomposition breaks down complex systems

into a hierarchical structure of simpler parts.

• Breaking a system into smaller parts enables users to understand, describe, and design complex systems.

• Functional decomposition consists of the following steps:

– Define the system context.

– This will help define the system boundaries.

– Describe the system in terms of high-level functions and their interfaces.

– Refine the high-level functions and partition them into smaller, more specific functions.

Functional Decomposition

Hierarchy Level 0(„Context-Diagram“)

External Data Sink

External Data Source

Hierarchical Structured Activity Chart

Bottom-Up

Top-Down

Hierarchy Level 1

Hierarchy Level 2

Language of StatemateFinite State Machines (FSM):

A virtual machine that can be in any one of a set offinite states and whose next states and outputs are functions of input and the current state.

Hierarchy:

Structure:A state may consist of states which consists of states….Priority Rule:Priority is given to the transition whose source and target states have a higher common ancestor state.

Concurrency:

“Processes that may execute in parallel on multipleprocessors or asynchronously on a single processor.” IEEE 729

S1 S2E1

E2

S1_S2

E1E2 F1F2

S1 S2

S11

S12

S21

S22

“History Connector”

S12_S3

S22S21

S1

E1

E2

E3

S2H

Formal Methods

Home assignments:

- 11.2 Textual specification- 11.18 Z-language

Please email to herttua@eurolock.org by 5 of April 2005

References: I-Logix, KnowGravity