Safety Critical Systems 4 Formal Methods / Modelling T

Formal Methods Formal methods have been used for safety and security- critical purposes during last decades for e.g: - Certifying the Darlington Nuclear Generating Station plant shutdown system. - Designing the software to reduce train separation in the Paris Metro. - Developing a collision avoidance system for United States airspace. - Assuring safety in the development of programmable logic controllers. - Developing a water level monitoring system. - Developing an air traffic control system.

-

Need for Formal Methods To mathematically describe the system – both software and hardware/functionality To mathematically describe the properties for validation/verification – possiblity to prove Enables simulation ( validation) Enables automatic verification

Formal Methods and Safety-Critical Systems - Formal Methods are used in expressing requirements, design and analysis of a safety critical software and hardware. The use of mathematical techniques reduce possible personal interpretation - There exists a need for using formal methods from writing requirements to verifying the system that they are fulfilling those - Many difficulties are related to misunderstanding requirements/specification.

Semi-formal Requirements/Specification Requirements should be unambiguous, complete, consistent and correct. - Natural language has the interpretation 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 Model Informal Verification Consistency Implement. Validation Verification (Testing) Consistency (another) Model  Formal Verification

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)

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 functions. - VDM (Vienna Development Method ISO standardised). - 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 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.

Formal 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 divided into smaller parts – schemas - These schemas describe the statical and dynamical characteristics of the system: static: possible states, invariants dynamic: possible operations, pre/post states -Z is an excellent tool for modelling data, state and operations

Simple example of Z notation ___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?} _________________________

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, e.g. 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.

Modelling Requirements Models needed for communication with domain experts (simulation) Automatic verification (model checker, theorem proving)

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

Verification and Validation - Verification – Are we building the system right? - Validation – Are we building the right system?

Verified software process

Model Verification e.g. „A point may never move when a route is locked.“ Challenger  Proof e.g. challenger is false in the following case: User: set route A System: steer point 1 left HW: point 1 at left User: set point 1 right System: steer point 1 right CONFLICT!!! Domain Expert Verifier Verification Support Tool Requirements Model Requirements Modeling Language

Languages of Logic –Propositional Logic Statements –(1st Order) Predicate Logic (FOPL) Statements quantified ( ,  ) over things (objects!) –Linear Temporal Logic (LTL) Statements quantified ( , , G, F, H, P) over things and time –Computational Tree Logic (CTL) Statements quantified ( , , G, F, H, P, ,  ) over things, time and worlds (modal logic) –Enhanced Regular Expression Logic (ERE) Statements about occurrence patterns (seq, sel, itr, par) of events and conditions causing actions Note: The list above is neither complete nor it does necessarily imply any hierarchy! S S t S t S t

(Some) Languages of Logic Objects ,  Time G, F, H, P Worlds ,  Propositional Logic Predicate Logic Modal Logic Temporal Logic (LTL) CTL ERE? DL

Verification Technologies Model Checking Theorem Proving Objects ,  Time G, F, H, P Worlds ,  Propositiona l Logic Predicate Logic Moda l Logic Temporal Logic (LTL) CTL ERE? DLDL

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 modelling Based on Harel state charts from 80‘s Functional decomposition Used years in aviation and car industry Mainly for simulating and validating functionality (Test cases) Model checker for verification

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. 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 S1S2 E1 E2 S1_S2 E1 E2F1F2 S1S2 S11 S12 S21 S22 “History Connector” S12_S3 S22S21 S1 E1 E2 E3 S2 H

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

System Development and Validation with STATEMATE closing the Loop via linear ‘Testbench Models’

System Validation: Generating Test-Data from Requirement Scenarios (Waveform Diagram derived from Trace-File ) Operational Input Operational Output Operational Input Operational Output Requirement 2 Requirement 1

Formal Methods Home assignments: 11.2 What problems are associated with specifications written in natural language? Explain what is meant by a 'schema' in Z, and describe its basic form. Please to by 27 of March 2008 References: I-Logix, KnowGravity,ITT