Specification Techniques

System models are abstract descriptions of systems whose requirements are being analyzed Objectives  To explain why specification modeling techniques help discover problems in system requirements  To describe –Behavioural modeling (Finite State Machines, Petri- nets), –Data modeling and –Object modeling (Unified Modeling Language, UML)

Formal Specification - Techniques for the unambiguous specification of software Objectives:  To explain why formal specification techniques help discover problems in system requirements  To describe the use of –algebraic techniques (for interface specification) and –model-based techniques (for behavioural specification)

System Modeling  System modeling helps the analyst to understand the functionality of the system and models are used to communicate with customers  Different models present the system from different perspectives –External perspective showing the system’s context or environment –Behavioural perspective showing the behaviour of the system –Structural perspective showing the system or data architecture

System Models Weaknesses  They do not model non-functional system requirements  They do not usually include information about whether a method is appropriate for a given problem  They may produce too much documentation  The system models are sometimes too detailed and difficult for users to understand

Model Types  Data processing model showing how the data is processed at different stages  Composition model showing how entities are composed of other entities  Architectural model showing principal sub-systems  Classification model showing how entities have common characteristics  Stimulus/response model showing the system’s reaction to events

Context Models  Context models are used to illustrate the boundaries of a system  Social and organizational concerns may affect the decision on where to position system boundaries  Architectural models show a system and its relationship with other systems

The Context of an ATM System

Process Models  Process models show the overall process and the processes that are supported by the system  Data flow models may be used to show the processes and the flow of information from one process to another

Equipment Procurement Process

Semantic Data Models  Used to describe the logical structure of data processed by the system  Entity-relation-attribute model sets out the entities in the system, the relationships between these entities and the entity attributes  Widely used in database design. Can readily be implemented using relational databases  No specific notation provided in the UML but objects and associations can be used

Software Design Semantic Model

Data Dictionary Entries Data dictionaries are lists of all of the names used in the system models Descriptions of the entities, relationships and attributes are also included

Object Models  Object models describe the system in terms of object classes  An object class is an abstraction over a set of objects with common attributes and the services (operations) provided by each object  Various object models may be produced –Inheritance models –Aggregation models –Interaction models

Object Models  Natural ways of reflecting the real-world entities manipulated by the system  More abstract entities are more difficult to model using this approach  Object class identification is recognized as a difficult process requiring a deep understanding of the application domain  Object classes reflecting domain entities are reusable across systems

The Unified Modeling Language  Devised by the developers of widely used object- oriented analysis and design methods  Has become an effective standard for object-oriented modeling  Notation –Object classes are rectangles with the name at the top, attributes in the middle section and operations in the bottom section –Relationships between object classes (known as associations) are shown as lines linking objects –Inheritance is referred to as generalization and is shown ‘upwards’ rather than ‘downwards’ in a hierarchy

Behavioural Models  Behavioural models are used to describe the overall behaviour of a system  Two types of behavioural model –Data processing models that show how data is processed as it moves through the system –State machine models that show the systems response to events  Both of these models are required for a description of the system’s behaviour

Data Flow Diagrams  Data flow diagrams are used to model the system’s data processing  These show the processing steps as data flows through a system  IMPORTANT part of many analysis methods  Simple and intuitive notation that customers can understand  Show end-to-end processing of data

Order Processing DFD

Data Flow Diagrams  DFDs model the system from a functional perspective  Tracking and documenting how the data associated with a process is helpful to develop an overall understanding of the system  Data flow diagrams may also be used in showing the data exchange between a system and other systems in its environment

State Machine Models  State Machine models the behaviour of the system in response to external and internal events  They show the system’s responses to stimuli so are often used for modeling real-time systems  State machine models show system states as nodes and events as arcs between these nodes. When an event occurs, the system moves from one state to another  State charts are an integral part of the UML

Microwave Oven Model State machine model does not show flow of data within the system

Microwave Oven Stimuli

Finite State Machines Finite State Machines (FSM), also known as Finite State Automata (FSA) are models of the behaviours of a system or a complex object, with a limited number of defined conditions or modes, where mode transitions change with circumstance

Finite State Machines - Definition A model of computation consisting of –a set of states, –a start state, –an input alphabet, and –a transition function that maps input symbols and current states to a next state  Computation begins in the start state with an input string. It changes to new states depending on the transition function. –states define behaviour and may produce actions –state transitions are movement from one state to another –rules or conditions must be met to allow a state transition –input events are either externally or internally generated, which may possibly trigger rules and lead to state transitions

Variants of FSMs  There are many variants, for instance, –machines having actions (outputs) associated with transitions (Mealy machine) or states (Moore machine), –multiple start states, –transitions conditioned on no input symbol (a null) or more than one transition for a given symbol and state (nondeterministic finite state machine), –one or more states designated as accepting states (recognizer), etc.

Finite State Machines with Output (Mealy and Moore Machines)  Finite automata are like computers in that they receive input and process the input by changing states. The only output that we have seen finite automata produce so far is a yes/no at the end of processing.  We will now look at two models of finite automata that produce more output than a yes/no.

Moore Machine  Basically a Moore machine is just a FA with two extras. 1. It has TWO alphabets, an input and output alphabet. 2. It has an output letter associated with each state. The machine writes the appropriate output letter as it enters each state. The output produced by the machine contains a 1 for each occurrence of the substring aab found in the input string. This machine might be considered as a "counting" machine.

Mealy Machine  Mealy Machines are exactly as powerful as Moore machines. –(we can implement any Mealy machine using a Moore machine, and vice versa).  However, Mealy machines move the output function from the state to the transition. This turns out to be easier to deal with in practice, making Mealy machines more practical.

A Mealy machine produces output on a transition instead of on entry into a state. Transitions are labelled i/o where –i is a character in the input alphabet and –o is a character in the output alphabet.  Mealy machine are complete in the sense that there is a transition for each character in the input alphabet leaving every state.  There are no accept states in a Mealy machine because it is not a language recognizer, it is an output producer. Its output will be the same length as its input. The following Mealy machine takes the one's complement of its binary input. In other words, it flips each digit from a 0 to a 1 or from a 1 to a 0.

State Charts  Allow the decomposition of a model into sub-models (see a figure)  A brief description of the actions is included following the ‘do’ in each state  Can be complemented by tables describing the states and the stimuli

Petri Nets Model  Petri Nets were developed originally by Carl Adam Petri, and were the subject of his dissertation in  Since then, Petri Nets and their concepts have been extended, developed, and applied in a variety of areas.  While the mathematical properties of Petri Nets are interesting and useful, the beginner will find that a good approach is to learn to model systems by constructing them graphically.

The Basics  A Petri Net is a collection of directed arcs connecting places and transitions.  Places may hold tokens.  The state or marking of a net is its assignment of tokens to places. Place with token P1 P2 T1 Arc with capacity 1 Transition Place

Capacity  Arcs have capacity 1 by default; if other than 1, the capacity is marked on the arc.  Places have infinite capacity by default.  Transitions have no capacity, and cannot store tokens at all.  Arcs can only connect places to transitions and vice versa.  A few other features and considerations will be added as we need them.

The Classical Petri Net Model A Petri net is a network composed of places ( ) and transitions ( ). t2 p1 p2 p3 p4 t3 t1 Connections are directed and between a place and a transition. Tokens ( ) are the dynamic objects. The state of a Petri net is determined by the distribution of tokens over the places.

Transition t1 has three input places (p1, p2 and p3) and two output places (p3 and p4). Place p3 is both an input and an output place of t1. p1 p2 p3 p4 t1

Enabling Condition Transitions are the active components and places and tokens are passive. A transition is enabled if each of the input places contains tokens. t1t2 Transition t1 is not enabled, transition t2 is enabled.

Firing An enabled transition may fire. Firing corresponds to consuming tokens from the input places and producing tokens for the output places. t2 Firing is atomic.

Example

Non-Determinism Two transitions fight for the same token: conflict. Even if there are two tokens, there is still a conflict. t1 t2

A Collection of Primitive Structures that occur in Real Systems

High-Level Petri Nets  The classical Petri net was invented by Carl Adam Petri in Since then a lot of research has been conducted (>10,000 publications).  Since the 80-ties the practical use is increasing because of the introduction of high-level Petri nets and the availability of many tools.  High-level Petri nets are Petri nets extended with –color (for the modeling of attributes) –time (for performance analysis) –hierarchy (for the structuring of models, DFD's)

Modeling States of a process are modeled by tokens in places and state transitions leading from one state to another are modeled by transitions.  Tokens represent objects (humans, goods, machines), information, conditions or states of objects.  Places represent buffers, channels, geographical locations, conditions or states.  Transitions represent events, transformations or transportations.

Example: Traffic Light rg red yellow green yr gy

 Current State The configuration of tokens over the places.  Reachable State A state reachable form the current state by firing a sequence of enabled transitions.  Dead State A state where no transition is enabled. Some Definitions blackred bbrr br

High-Level Petri Nets In practice the classical Petri net is not very useful:  The Petri net becomes too large and too complex.  It takes too much time to model a given situation.  It is not possible to handle time and data. Therefore, we use high-level Petri nets, i.e. Petri nets extended with:  color  time  hierarchy

To explain the three extensions we use the following example of a hairdresser's saloon. start waiting finish busy free ready client waiting hairdresser ready to begin Note how easy it is to model the situation with multiple hairdressers.

The Extension with Color A token often represents an object having all kinds of attributes. Therefore, each token has a value (color) which refers to specific features of the object modeled by the token. start waiting finish busy free ready name: Harry age: 28 experience: 2 name: Sally age: 28 hairtype: BL

Each transition has an (in)formal specification which specifies:  the number of tokens to be produced,  the values of these tokens,  and (optionally) a precondition. The complexity is divided over the network and the values of tokens. This results in a compact, manageable and natural process description.

Examples c := a+b a b c + b := -a b-a if a> 0 then b:= a else c:=a fi a b c select a >=0 | b :=  a bsqrta Extra Credit Exercise: calculate  |a+b| using these building blocks

The Extension with Time For performance analysis we need to model durations, delays, etc. Therefore, each token has a timestamp and transitions determine the delay of a produced token. start waiting finish busy free ready  =3  =0

The Extension with Hierarchy  A mechanism to structure complex Petri nets comparable to DFD's.  A subnet is a net composed out of places, transitions and subnets. waitingready h1 h2 h3 startfinishbusy free

Key Points  Modeling specification complements informal requirements elicitation techniques.  Model specifications can be precise and unambiguous, but generally depend on interpretation of inputs/output. They reduce areas of doubt in a specification.  More formal models, such as FSM or Petri nets forces an analysis of the system requirements at an early stage. Correcting errors at this stage is cheaper than modifying a system during design.