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Producibility
Constraints
Production
Requirements
In-service
Experience
Resolution
Issue
Lessons
Learned
Accidents
Incidents
and
Technology
Changes
Market Driven
Requirements
Airline
Industry
Trends
Requirements
Customer
Public
Perceptions
Regulatory
Requirements
Political
World
Airports and
Groundside
Requirements
Airspace
and ATC
Requirements
Infrastructure
Requirements
Boeing
Ensuring a Successful Product
Right Product
Appropriate and
Validated Requirements
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Allocated
Requirements
FHA
Trees
Fault
FMEA
Preliminary
Validate
Analyze and
Compliance
Requirements
Testing
Verification
Certification
Product
Successful
Design
Detailed
Safety Reliability
Availability
Maintainability
Supportability
Analyses
Physical and
Preliminary
Functional Def.
Product Right
Types of Specifications
Informal
Free form, natural language
Ambiguity and lack of organization can lead to
incompleteness, inconsistency, and misunderstandings
Formatted
Standardized syntax (e.g., UML)
Basic consistency and completeness checks
Imprecise semantics implies other sources of error
may still be present.
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Intent Specifications
Part-Whole
Blackbox
Behavior
Physical
Representation
Principles
System Design
Purpose
System
Design
Representation
SystemOperatorEnvironment
Verification
Validation
Refinement
Operations
Intent
Each level supports a different type of reasoning about system.
Mappings between levels provide relational info necessary to
reason across hierarchical levels.
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Types of Specifications (2)
Formal
Syntax and semantics rigorously defined.
Precise form, perhaps mathematical.
Eliminate imprecision and ambiguity.
Provide basis for mathematically verifying equivalence
between specification and implementation.
May be hard to read without training.
Semantic distance too great?
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INPUT SPACE
OUTPUT SPACE
I
OF
F(I) = O
A program is a mathematical object
A programming language is a mathematical language.
Therefore, we can prove properties about the program.
e.g. does it do what it is supposed to do
does it not do anything harmful
Building a model like engineers do, but need discrete rather than
continuous mathematics.
Copyright Nancy Leveson, Sept. 1999
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Formal Specifications
Goal: Describe external behavior without describing or
constraining internal design (implementation).
Formal method has 2 parts:
1. Logical theory: means by which reason about specs,
properties, and programs.
First-order predicate calculus (quantification over variables)
Second-order predicate calculus (quantification over relations)
Temporal logic
2. Structuring theory: defines elements being reasoned about
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Structuring Theory
1. Descriptive Specifications: State desired properties in a
purely declarative way.
Input-output assertions
Algebraic specifications (set of axioms)
2. Operational Specification: Describe desired behavior by
providing a model of system.
Abstract Model (in terms of previously defined mathematical
objects, e.g., sets and sequences
operations, e.g., functions and mappings)
State machine (states and transitions between states)
Copyright Nancy Leveson, Sept. 1999
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Input-Output Assertions
S {P} Q
If S holds before execution of S, then Q holds afterward.
Examples:
n
sum =
a
j
j=1
1. sum = 0 { for i=1 to n do sum:=sum+a(i) }
2. proc search(A,n,x) int;
pre n 0
(result = 0
(result = i
i {1,...,i-1} : A[i] = x)
{1,...,n} : A[i] = x)i post
1 i n A[i] = x
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Copyright Nancy Leveson, Sept. 1999
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Algebraic Specifications
Uses: (1) set of objects
(2) set of operations
(3) axioms specifying behavior of operations
Two parts to a specification:
syntax
axioms
Example: STACK
Intuitive definitions of stack operations:
NEW creates an empty stack
PUSH adds a new item to top of stack
TOP returns a copy of top item
POP removes top item
Empty tests for an empty stack
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Algebraic Specifications (2)
SYNTAX:
OPERATION DOMAIN RANGE
New ( ) Stack
Push
Pop
Top
Empty
(Stack, Item) Stack
(Stack) Stack
(Stack) Item
(Stack) Boolean
AXIOMS: (stk is of type Stack, itm is of type Item)
1. Empty (new) = true
2. Empty (push (stk,itm)) = false
3. Pop (new) = error
4. Top (new) = error
5. Pop (Push (stk,itm)) = stk
6. Top (Push (stk,itm)) = itm
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Copyright Nancy Leveson, Sept. 1999
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Algebraic Specifications (3)
Axioms stated in English:
1. A new stack is empty.
2. A stack is not empty immediately after pushing
an item onto it.
3. Attempting to pop a new stack results in an error.
4. There is no top item on a new stack.
5. Pushing an item onto a stack and immediately popping
it off leaves the stack unchanged.
6. Pushing an item onto a stack and immediately
requesting the top item returns the item just pushed
onto the stack.
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Algebraic Specifications (4)
If want to add an operator Replace (stk,itm):
Replace (stk,itm) = if Empty (stk) then error
else Push (Pop (stk),itm)
What does this do (in English)?
Canonical Form: A particular stack written in terms of
the operations used to form it.
A = = (Push (Push (Push (New,a)), b), c), d)
Top (Pop (Pop A)) = b
d
c
b
a
c
Copyright Nancy Leveson, Sept. 1999
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