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- Usability

Where Formal Method applied?
- In various aspects of a large complex system such as safety-critical system.

Critical system: 

Mathematical modelling techniques
– model oriented (VDM, Z)

Semantic – Method of structuring data -> represent in logical way

Modelling Language -> mathematic + semantic

·        Informal

·        Low

·        Medium

·        High

Formal Methods Model – Mathematical methods/techniques -> process developing complex systems

·        Use formal specification language -> define characteristic

Formalize – Models of requirements knowledge

·        What? -> modelling + evaluation

·        Specifications of program design -> remove/exclude module/function in design

·        Why? -> 1. Removes ambiguity and improve proves (remove flaw)

  2. Verify the requirement (behaviour)

  3.  Execute specifications (avoid critical issues) -> record assumption + decisions

·        Not? -> Confuse which tool appropriate + Costly and unfeasible + Concentrate consistent

 

1.      Formal Specification Languages (Ex. Larch)

·        Good specify behavior program units Key -> Type checking / Theorem proving

·        Grew on program verification Spwaned

2.      Reactive System Modelling – Formalize dynamic models system behavior (Ex. RSML)

·        Good reactive system (Ex. Real-time)

·        Key: Consistency / Model Checking (abstraction)

·        Applicable to Requirements Languages

3.      Formal Conceptual Modelling – Capture real-world knowledge (Ex. Telos)

·        Use first order predicate logic

·        Key: Inference engines/default reasoning/KBS-shells

·        Applicable to Requirements Capture

1.      Formal Specification - translation of non-mathematical description into a formal specification language (ex. diagrams) 

-        Represents description - high-level behavior / properties system 

-        Well-defined language semantics

-        Type

o   Model Oriented - Construct a model of the system (Statecharts / Petri Nets)

o   Property Oriented - Set of necessary properties such as axioms (Algebraic semantics / Temporal logic models)

2.      Formal Proofs – Constructed small steps using small set of rules 

-        usually constructed with automated assistance

3.      Model Checking – 

-        Approaches – 1. Temporal model checking / 2. Automaton model checking 

-        Model Checkers – SMV-Symbolic Model Verification (Kripke Model) 

4.      Abstraction 

-        Representation smaller model

-        Focus on central properties + characteristics

·        Capture essential characteristics + ignore irrelevant details

·        Analyzed using mathematical reasoning -> prove system properties

-        Type – 1. Continuous models / 2. Discrete Models

1.      Expose defects

2.      Identify exceptions

3.      Evaluate test coverage

1.      Requires a sound mathematical knowledge of the developer 

2.      Different aspects design, different formal specification methods

3.      Cannot guarantee the completeness of a specifications

 

 

-MUHAMMAD HAFIZ BIN BASIRIN (D20201094848)- 

 

D20201092354 

Formal notations definition is "a general description of the use of mathematical notations such as logic and set theory to describe system specifications and software designs together with techniques of validation and verification based on mathematics".

Notations such as AUTOMATIC SIMULATION MODEL (ASM), B-METHOD and ACTOR MODEL. 

The need for a formal semantic definition also means that the specification languages cannot be based on natural language; it must be based on mathematics.

The extent to which formal methods are implemented can vary. Sometimes, the full implementation of formal methods is deemed too costly except in the case of critically important systems and complex designs where errors can result in costly redesigns or refabrication.


Some examples of systems that might be fully specified under formal methods would be complex semi-conductors such as CPUs, GPUs or even critical systems in software like that which is used in SCADA (Supervisory Control and Data Acquisition) for control of power plants and so on.

VDM Specification Language – Analysis design + identification key features (defects (early stage development))

·        Language = formal semantics + enabling proof properties model

·        Executable subset -> Analyzed (testing) + Executed (Graphical user interface)

VDM++ - Describe desired behavior system in abstract term

·        Functions = specified implicitly -> pre- and post- conditions 

VDM-SL Structure – Conventional modular extension = informative annex contains different structure principle

·        Module naming – Start = Keyword module -> name & End = Keyword end -> name

·        Importing – Import Section -> Start + Keyword import -> sequence import (Start = Keyword = name + signature)

·        Exporting – Other module have access -> exported <- Keyword export -> export module signature

·        More exotic features – Support parameterized+ instantiations modules

1.      Hard to use in industrial application

2.      Substantial number of tool challenges

VDM++ Structure - Traditional object-oriented structing

·        Class – Start class = Keyword class -> name of class & End class = Keyword -> again name class

·        Inheritance – Class name preceded keyword subclass -> comma-separated list + superclass name (class heading)

·        Access modifiers – Information hiding – private/public/protected

Functional Modeling – Functions are defined over data types

·        Main mechanism = implicit function definition

·        Required = deterministic (satisfy example must return same results same input)

State-based modeling – Functions = not have side effects, operations -> change state variables (AKA global)

Basic Types – Represent values cannot be decomposed – Ex. Bool/int/char

1.      Numeric types – unbounded with no maximum value – Ex. Nat1/nat/rat/real

2.      Constructed types – Created from basic types -> mappings/sequences/sets

a)      Union types – Contains all values = possible construct -> using non-disjoint types (int/nat)

b)     Types invariants – Boolean predict – restricts extent type being defined 

 

-MUHAMMAD HAFIZ BIN BASIRIN (D20201094848)-

 

Schemes – Specification building blocks (Invariants predicate = Boolean expressions)

·        Graphical presentation -> make specifications easier to understand

·        Mathematical notation -> allow completeness/consistency proof -> validate

schema includes 

·        A name identifying the schema  

·        A signature introducing entities and their types  

·        A predicate part defining invariants over these entities 

·        Marks before a schema,  

·        Delta (D) means changes 

·        Xi (X) means no changes  

·        Marks after a state variable, 

·        ? means input  

·        ! means output 

·        ‘ represents the value of the variable after an operation

Container = [content: N; capacity: N | content <= capacity] Ù

Indicator = [light:{off,on};reading: N; dangerLevel: N | light = on Û reading >= dangerLevel] 

·        danger level -> warning light on -

StorageTank = [DContainer; DIndicator | reading=content; capacity=250000; dangerLevel = 245000] FillOK = [DStorageTank; amount?: N | contents + amount? <= capacity; content’ = content +amount? 

OverFill = [XStorageTank; amount?: N; r!: seq CHAR | capacity < contents + amount?; r! =“Insufficient tank capacity – Fill cancelled” 

Fill = [FillOK Ú OverFill]

 

·        “normal” operation = schema

·        Schema for exceptional situations

·        Specified incrementally = separate schema -> combined -> produce complete

·        Combine all schemas using disjunction (or)

-MUHAMMAD HAFIZ BIN BASIRIN (D20201094848)-

Variables – Symbol stands for an individual in a collection or set (Ex. X = Monday)

·        Use letters at end

·        Collection of objects = domain of objects

Statement – Declarative sentence having truth value

Quantifiers – Propositional (well-formed formula) (finite sequence) have rather limited expressive power (For every x, x > 0)

Type:

·        Universal Quantifier (for all / for every / for any) - Ɐ

·        Existential Quantifier (for some / there exist / there is a / for at least) - ⱻ

Predicate – portion of a statement that give information about the subject (Ex. P(x) / R(x, y)) -> predicate symbols / predicate  variables 

·        Represented by letter P(x) -> used present unspecified property/predicate that x may have

·        Quantifier + predicate = complete statement

·        Collection of objects = domain of interpretation = at least one object

·        Predicate instantiated = proposition (variables = specific values)

·        Predicate logic extends more powerful than propositional logic

Unary Predicates – predicates involving properties of a single variable

Binary Predicate – (Ɐx)(ⱻy)Q(x,y) = for every x there exists a y such that Q(x,y)

Negation - Ɐx, ⱻy, P(x,y) = ⱻx, Ɐy, Px,y

Interpretation – Collection of objects = domain of interpretation (at least one object) / assignment of a property of object in domain / constant symbol in expression

·        Use logical connectives + predicates + quantifiers

·        Obey the rules of syntax to be considered a wff = (Ɐx)[P(x) -> Q(x)]

Validity – Analogous to a tautology of propositional logic = (Ɐx)P(x)  -> (ⱻx)P(x)

·        Truth predicate wff depend on interpretation

·        A valid predicate wff is instrinsically true

Truth values – True or false = depends on truth value of statement

Intrinsic truth – True for all truth values

Methodology – truth table determine tautology

Tautology -  Propositional formula that is true under any possible Boolean valuation of its propositional variables

         
MUHAMMAD HAFIZ BIN BASIRIN D20201094848