Safety-Critical Systems 4 Formal Methods / Modelling

1. Safety-Critical Systems 4Formal Methods / Modelling T 79.232

2. 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)

4. 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)

5. 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).

6. Domain Expert(s) Validation Validation Validation Text Informal Verification Model Verification (Testing) Formal Verification Implement. Consistency  Consistency (another) Model Consistency

7. Formal Methods/ Model orientated These 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

8. 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)

9. 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.

10. 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

11. 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, invariants dynamic: possible operations, pre/post states Z is an exellent tool for modelling data, state and operations

12. ___BirthdayBook_______ known:PNAME birthday: NAME ‌→ DATE _____________________ known = dom birthday _____________________ ___AddBirthday________ ∆BirthdayBook name?:NAME date?:DATE _____________________ name? /€ known birthday’ =birthdayU{name?‌→date?} _____________________ ___FindBirthday____________ ΞBirthdayBook name?:NAME date!:DATE _________________________ name?€ known date! = birthday(name?) _________________________ ___Remind________________ Ξ BirthdayBook today?:DATE cards!:PNAME _________________________ cards!={n:known|birthday(n)=today?} _________________________ Simple example of Z notation

13. 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.

14. 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.

15. Modeling Requirements • Models needed for communicating with domain experts (simulation) • Automatic verification (model checker, theorem proving)

16. versus Decomposition: Functional Glass Box versus View point:  Black Box Blabla  GFHP  Object-based versus Representation: Textual Graphical Some Modeling Styles

17. 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, …

18. 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

19. 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.

20. Functional Decomposition External Data Sink Hierarchy Level 0 („Context-Diagram“) External Data Source Top-Down Hierarchy Level 1 Hierarchy Level 2 Bottom-Up Hierarchical Structured Activity Chart

21. E1 S1 S2 E2 S12_S3 S1 E3 S2 E1 S21 S22 E2 S1_S2 H S1 S2 S11 S21 E1 E2 F2 F1 S12 S22 Language of Statemate Finite State Machines (FSM): A virtual machine that can be in any one of a set of finite states and whose next states and outputs are functions of input and the current state. “History Connector” 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 multiple processors or asynchronously on a single processor.” IEEE 729

22. 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