Software Testing Methodologies�

UNIT-7 STATES, STATE GRAPHS, AND TRANSITION TESTING

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Compiled with reference from:

Software Testing Techniques: Boris Beizer

Craft of Software Testing: Brain Marrick

Contents

• SYNOPSIS
• MOTIVATIONAL OVERVIEW
• STATE GRAPHS
• GOOD STATE GRAPHS AND BAD
• STATE TESTING
• TESTABILITY TIPS

SYNOPSIS

• The state graph and its associated state table are useful models for describing software behavior.
• The finite-state machine is a functional testing tool and testable design programming tool

MOTIVATIONAL OVERVIEW

• The finite-state machine is as fundamental to software engineering as boolean algebra.
• State testing strategies are based on the use of finite-state machine models for software structure, software behavior, or specifications of software behavior.
• Finite-state machines can also be implemented as table-driven software, in which case they are a powerful design option. Independent testers are likeliest to use a finite-state machine model as a guide to the design of functional tests—especially system tests.

STATE GRAPHS

• States
• Inputs and Transitions
• Outputs
• State Tables
• Time Versus Sequence
• Software Implementation

1. Implementation and Operation

2.Input Encoding and Input Alphabet

3.Output Encoding and Output Alphabet

4.State Codes and State-Symbol Products

5.Application Comments for Designers

6.Application Comments for Testers

�STATE GRAPHS�States

• The word “state” is used in much the same way it’s used in ordinary English, as in “state of the union,” or “state of health.”
• The Oxford English Dictionary defines “state” as: “A combination of circumstances or attributes belonging for the time being to a person or thing.”
• A program that detects the character sequence “ZCZC” can be in the following states:
• 1.  Neither ZCZC nor any part of it has been detected.
• 2.  Z has been detected.
• 3.  ZC has been detected.
• 4.  ZCZ has been detected.
• 5.  ZCZC has been detected

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Figure11.1

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STATE GRAPHS�States(continued)

• A moving automobile whose engine is running can have the following states with respect to its transmission:

1.  Reverse gear

2.  Neutral gear

3.  First gear

4.  Second gear

5.  Third gear

6.  Fourth gear

• Like,
• A person’s checkbook can have the what states with respect to the bank balance?
• A word processing program menu can be in the what states with respect to file manipulation?

�STATE GRAPHS�Inputs and Transitions

• Result of those inputs, the state changes, or is said to have made a transition. Transitions are denoted by links that join the states
• A finite-state machine is an abstract device that can be represented by a state graph having a finite number of states and a finite number of transitions between states.
• The ZCZC detection example can have the following kinds of inputs:
• 1.  Z
• 2.  C
• 3.  Any character other than Z or C, which we’ll denote by A

�STATE GRAPHS�Inputs and Transitions

• The state graph of Figure 11.1 is interpreted as follows:
• 1.  If the system is in the “NONE” state, any input other than a Z will keep it in that state.
• 2.  If a Z is received, the system transitions to the “Z” state.
• 3.  If the system is in the “Z” state and a Z is received, it will remain in the “Z” state. If a C is received, it will go to the “ZC” state; if any other character is received, it will go back to the “NONE” state because the sequence has been broken.
• 4.  A Z received in the “ZC” state progresses to the “ZCZ” state, but any other character breaks the sequence and causes a return to the “NONE” state.
• 5.  A C received in the “ZCZ” state completes the sequence and the system enters the “ZCZC” state. A Z breaks the sequence and causes a transition back to the “Z” state; any other character causes a return to the “NONE” state.
• 6.  The system stays in the “ZCZC” state no matter what is received.

STATE GRAPHS�Outputs

• An output^* can be associated with any link. Outputs are denoted by letters or words and are separated from inputs by a slash as follows: “input/output.”

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• The state graph is shown in Figure 11.2.
• As in the previous example, the inputs and actions have been simplified. There are only two kinds of inputs (OK, ERROR) and four kinds of outputs (REWRITE, ERASE, NONE, OUT-OF-SERVICE).

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STATE GRAPHS�State Tables

1.  Each row of the table corresponds to a state.

2.  Each column corresponds to an input condition.

3.  The box at the intersection of a row and column specifies the next state (the transition) and the output, if any

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STATE GRAPHS�Time Versus Sequence

Although the finite-state machine model can be elaborated to include notions of time in addition to sequence, such as timed Petri nets

Software Implementation�1.Implementation and Operation

• There are four tables involved:
• 1.  A table or process that encodes the input values into a compact list (INPUT_CODE_TABLE).
• 2.  A table that specifies the next state for every combination of state and input code (TRANSITION_TABLE).
• 3.  A table or case statement that specifies the output or output code, if any, associated with every state-input combination (OUTPUT_TABLE).
• 4.  A table that stores the present state of every device or process that uses the same state table—e.g., one entry per tape transport (DEVICE_TABLE).

Software Implementation�1.Implementation and Operation

• The routine operates as follows, where # means concatenation:
• BEGIN
• PRESENT_STATE := DEVICE_TABLE(DEVICE_NAME)
• ACCEPT INPUT_VALUE
• INPUT_CODE := INPUT_CODE_TABLE(INPUT_VALUE)
• POINTER := INPUT_CODE#PRESENT STATE
• NEW_STATE := TRANSITION_TABLE(POINTER)
• OUTPUT_CODE := OUTPUT_TABLE(POINTER)
• CALL OUTPUT_HANDLER(OUTPUT_CODE)
• DEVICE_TABLE(DEVICE_NAME) := NEW_STATE
• END

Software Implementation�1.Implementation and Operation

• 1.  The present state is fetched from memory.
• 2.  The present input value is fetched. If it is already numerical, it can be used directly; otherwise, it may have to be encoded into a numerical value, say by use of a case statement, a table, or some other process.
• 3.  The present state and the input code are combined (e.g., concatenated) to yield a pointer (row and column) of the transition table and its logical image (the output table).
• 4.  The output table, either directly or via a case statement, contains a pointer to the routine to be executed (the output) for that state-input combination. The routine is invoked (possibly a trivial routine if no output is required).
• 5.  The same pointer is used to fetch the new state value, which is then stored.

Software Implementation�2.Input Encoding and Input Alphabet

• The alternative to input encoding is a huge state graph and table because there must be one outlink in every state for every possible different input.
• Input encoding compresses the cases and therefore the state graph.
• Another advantage of input encoding is that we can run the machine from a mixture of otherwise incompatible input events, such as characters, device response codes, thermostat settings, or gearshift lever positions.
• The set of different encoded input values is called the input alphabet.

Software Implementation�3.Output Encoding and Output Alphabet

• There are only a finite number of such distinct actions, which we can encode into a convenient output alphabet.

Software Implementation�4.State Codes and State-Symbol Products

• The term state-symbol product is used to mean the value obtained by any scheme used to convert the combined state and input code into a pointer to a compact table without holes.
• “state codes” in the context of finite-state machines, we mean the (possibly) hypothetical integer used to denote the state and not the actual form of the state code that could result from an encoding process.

Software Implementation�5. Application Comments for Designers

• State-table implementation is advantageous when either the control function is likely to change in the future or when the system has many similar, but slightly different, control functions.
• This technique can provide fast response time—one pass through the above program can be done in ten to fifteen machine instruction execution times.
• It is not an effective technique for very small (four states or less) or big (256 states or more) state graphs.

Software Implementation�6. Application Comments for Testers

• Independent testers are not usually concerned with either implementation details or the economics of this approach but with how a state-table or state-graph representation of the behavior of a program or system can help us to design effective tests.
• There is an interesting correlation, though: when a finite-state machine model is appropriate, so is a finite-state machine implementation.

GOOD STATE GRAPHS AND BAD�1. General

• 1.  The total number of states is equal to the product of the possibilities of factors that make up the state.
• 2.  For every state and input there is exactly one transition specified to exactly one, possibly the same, state.
• 3.  For every transition there is one output action specified. That output could be trivial, but at least one output does something sensible.^*
• 4.  For every state there is a sequence of inputs that will drive the system back to the same state.^**

• Figure 11.3 shows examples of improper state graphs.

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GOOD STATE GRAPHS AND BAD�2.State Bugs�2.1Number of States

• A state graph consists of the number of states that are essential to identify or model the behavior of system .
• In practice, the state is directly or indirectly recorded as a combination of values of variables that appear in the data base. State table is used to record the values of variables or number of states of the state graph.
• If the no.of states are not recorded or missed then the result might be the bugs for identifying the behavior of each state, transition, output of the state graph.
• Find the number of states as follows:
• 1.  Identify all the component factors of the state.
• 2.  Identify all the allowable values for each factor.
• 3.  The number of states is the product of the number of allowable values of all the factors.

Functional specifications are used to find

• factors of the state
• number of possible values for each factor

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GOOD STATE GRAPHS AND BAD�2.State Bugs�Impossible States

There are some combinations of factors that are impossible. The states inclusion of

these factors are known as impossible states. Impossible states do not have specific meaning in the system.

• If the power supply is damaged then there is no use of considering the factors of damaged power supply.�The combination of factors for power supply reduced 3 states (4 states).�These factors caused to the overall behavior of the system.

GOOD STATE GRAPHS AND BAD�2.State Bugs�Equivalent States

• Two states are equivalent if every sequence of inputs starting from one state produces exactly the same sequence of outputs when started from the other state.

GOOD STATE GRAPHS AND BAD�2.State Bugs�Equivalent States

• Equivalent states can be recognized by the following procedures:
• 1.  The rows corresponding to the two states are identical with respect to input/output/next state but the name of the next state could differ. The two states are differentiated only by the input that distinguishes between them. This situation is shown in Figure 11.6. Except for the a,b inputs, which distinguish between states A and B, the system’s behavior in the two states is identical for every input sequence; they can be merged.
• 2.  There are two sets of rows which, except for the state names, have identical state graphs with respect to transitions and outputs. The two sets can be merged (see Figure 11.7).

GOOD STATE GRAPHS AND BAD�2.State Bugs�Equivalent States

• Equalent states

GOOD STATE GRAPHS AND BAD�2.State Bugs�Equivalent States

• Unmergable procedure

GOOD STATE GRAPHS AND BAD�2.State Bugs�Equivalent States

GOOD STATE GRAPHS AND BAD�3.Transition Bugs�1. Unspecified and Contradictory Transitions

• Exactly one transition must be specified for every combination of input and state.
• A program can’t have contradictions or ambiguities. Ambiguities are impossible because the program will do something (right or wrong) for every input.

GOOD STATE GRAPHS AND BAD�3.Transition Bugs�3.2An Example

• Specifications are one of the most common source of ambiguities and contradictions.
• the first statement of the specification:
• Rule 1: The program will maintain an error counter, which will be incremented whenever there’s an error.

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GOOD STATE GRAPHS AND BAD�3.Transition Bugs�3.2An Example

There are only two input values, “okay” and “error.”

GOOD STATE GRAPHS AND BAD�3.Transition Bugs�3.2An Example

• Adding rule 2, we get

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GOOD STATE GRAPHS AND BAD�3.Transition Bugs�3.2An Example

GOOD STATE GRAPHS AND BAD�3.Transition Bugs�3.2An Example

GOOD STATE GRAPHS AND BAD�3.Transition Bugs�3.2An Example

Rule 3, if followed blindly, causes an unnecessary rewrite. It’s a minor bug, so let it go for now, but it pays to check such things. There might be an arcane security reason for rewriting, erasing, and then rewriting again.

GOOD STATE GRAPHS AND BAD�3.Transition Bugs�3.2An Example

Rule 4 terminates our interest in this state graph so we can dispose of states beyond 6. The details of state 6 will not be covered by this specification; presumably there is a way to get back to state 0. Also, we can credit the specifier with enough intelligence not to have expected a useless rewrite and erase prior to going out of service.

GOOD STATE GRAPHS AND BAD�3.Transition Bugs�3.2An Example

Rule 7: If the rewrite was successful, decrement the error counter and return to the previous state.

Rule 7 got rid of the ambiguities but created contradictions. The specifier’s intention was probably:

Rule 7A: If there have been no erasures and the rewrite is successful, return to the previous state.

GOOD STATE GRAPHS AND BAD�3.Transition Bugs�3.2An Example

GOOD STATE GRAPHS AND BAD�3.Transition Bugs�3.3 unreachable state

• An unreachable state is like unreachable code—a state that no input sequence can reach.
• An unreachable state is not impossible, just as unreachable code is not impossible.

GOOD STATE GRAPHS AND BAD�3.Transition Bugs�3.4 Dead States

• A dead state, (or set of dead states) is a state that once entered cannot be left.

GOOD STATE GRAPHS AND BAD�4. Output Errors

• The states, the transitions, and the inputs could be correct, there could be no dead or unreachable states, but the output for the transition could be incorrect.

GOOD STATE GRAPHS AND BAD�5. Encoding Bugs

• The behavior of a finite-state machine is invariant under all encodings. That is, say that the states are numbered 1 to n.

STATE TESTING�1.Impact of Bugs

• 1.  Wrong number of states.
• 2.  Wrong transition for a given state-input combination.
• 3.  Wrong output for a given transition.
• 4.  Pairs of states or sets of states that are inadvertently made equivalent (factor lost).
• 5.  States or sets of states that are split to create inequivalent duplicates.
• 6.  States or sets of states that have become dead.
• 7.  States or sets of states that have become unreachable.

STATE TESTING�2. Principles

• The starting point of state testing is:
• 1.  Define a set of covering input sequences that get back to the initial state when starting from the initial state.
• 2.  For each step in each input sequence, define the expected next state, the expected transition, and the expected output code.
• A set of tests, then, consists of three sets of sequences:
• 1.  Input sequences.
• 2.  Corresponding transitions or next-state names.
• 3.  Output sequences.

STATE TESTING �3. Limitations and Extensions

• 1.  Simply identifying the factors that contribute to the state, calculating the total number of states, and comparing this number to the designer’s notion catches some bugs.
• 2.  Insisting on a justification for all supposedly dead, unreachable, and impossible states and transitions catches a few more bugs.
•   Insisting on an explicit specification of the transition and output for every combination of input and state catches many more bugs.
• 4.  A set of input sequences that provide coverage of all nodes and links is a mandatory minimum requirement.
• 5.  In executing state tests, it is essential that means be provided (e.g., instrumentation software) to record the sequence of states (e.g., transitions) resulting from the input sequence and not just the outputs that result from the input sequence.

STATE TESTING �4.What to Model

• 1.  Any processing where the output is based on the occurrence of one or more sequences of events, such as detection of specified input sequences, sequential format validation, parsing, and other situations in which the order of inputs is important.
• 2.  Most protocols between systems, between humans and machines, between components of a system (CHOI84, CHUN78, SARI88).
• 3.  Device drivers such as for tapes and discs that have complicated retry and recovery procedures if the action depends on the state.
• 4.  Transaction flows where the transactions are such that they can stay in the system indefinitely—for example, online users, tasks in a multitasking system.
• 5.  High-level control functions within an operating system. Transitions between user states, supervisor’s states, and so on. Security handling of records, permission for read/write/modify privileges, priority interrupts and transitions between interrupt states and levels, recovery issues and the safety state of records and/or processes with respect to recording recovery data

• 6.  The behavior of the system with respect to resource management and what it will do when various levels of resource utilization are reached. Any control function that involves responses to thresholds where the system’s action depends not just on the threshold value, but also on the direction in which the threshold is crossed. This is a normal approach to control functions
• 7.  A set of menus and ways that one can go from one to the other. The currently active menus are the states, the input alphabet is the choices one can make, and the transitions are invocations of the next menu in a menu tree. Many menu-driven software packages suffer from dead states—menus from which the only way out is to reboot.
• 8.  Whenever a feature is directly and explicitly implemented as one or more state-transition tables.

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STATE TESTING �4.What to Model

STATE TESTING �5. Getting the Data

• State testing, more than most functional test strategies, tends to have a labor-intensive data-gathering phase and tends to need many more meetings to resolve issues.

STATE TESTING �6. Tools

• There are tools to do the same for hardware logic designs.
• That’s the good news.
• The bad news is that these systems and languages are proprietary, of the home-brew variety, internal, and/or not applicable to the general use of software implementations of finite-state machines

TESTABILITY TIPS�1. A Balm for Programmers

• The key to testability design is easy: build explicit finite-state machines.

TESTABILITY TIPS�2. How Big, How Small?���

• There are about eighty possible good and bad three-state machines, 2700 four-state machines, 275,000 five-state machines, and close to 100 million six-state machines, most of which are bad.

TESTABILITY TIPS�3. Switches, Flags, and Unachievable Paths

• Figure 11.9.  Program with One Switch Variable.

Switches, Flags, and Unachievable Paths�(continued)

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• Three-Switch- Variable Program.

�TESTABILITY TIPS�3.Switches, Flags, and Unachievable Paths

•  Switches in a Loop.

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TESTABILITY TIPS�4. Essential and Inessential Finite-State Behavior

• The simplest essential finite-state machine is a flip-flop. There is no logic that can implement it without some kind of feedback.
• we cannot describe this behavior by a decision table or decision tree unless you provide feedback into the table or call it recursively.

• FSM is an important mechanism in s/w engineering as functional and programming testing tool.
• FSM can be represented by a state graph which consists of finite no. of states as well as a finite no. of transitions b/w those states and actions.
• It is essential tool for state testing in order to identify or model the behaviour of s/w.
• It is stated that any encoding process does not change the consistency of a FSM.

Design Guidelines

• The following are the design guidelines for building FSM into user code. They are,
• Initially, learn the procedure of FSM that are used in both h/w and s/w.
• Design an abstract machine model in such away, that it works properly and satisfies the user requirements. Then use State graph or state table to analyse the large no. of states based on the abstract machine model.
• Design an explicit FSM which comprises input encoding, output encoding, state code, state symbol product, transition table, output table and state storage.
• Prototype test must be conducted thoroughly to determine the processing time and space of explicit FSM design.

Finite State Machine

5. If time or space is more effecting the overall system, then use shortcuts to complete the design process. It can be achieved by implicit design of FSM in the following order i.e., output encoding, input encoding, state code, state symbol product, output table, transition table and state storage.

6. If there are more than a few number of states then use hierarchical design to represent them.

7. If there are large no. of states then s/w tools and programming languages must be developed or purchased in order to implement the FSM.

8. The capability to initialize to any arbitrary state must be inbuilt together with the transition verification instrumentation. These are much easier to do with an explicit machine.

• FSM supports distinct encoding methods.
• The fields are implemented as group of bits/byte specifying the potential size of the code i.e., encoding is performed ,if code values are less than the potential size . This is done even if the code values are out of the field.
• For instance , encoding process is strongly typed languages with user defined types is a conversion from set membership to a pointer type or integer type.

TESTABILITY TIPS�5. Design Guidelines

• 1..  Start by designing the abstract machine. Verify that it is what you want to do. Do an explicit analysis, in the form of a state graph or table, for anything with three states or more.
• 2.  Start with an explicit design—that is, input encoding, output encoding, state code assignment, transition table, output table, state storage, and how you intend to form the state-symbol product. Do this at the PDL level. But be sure to document that explicit design.
• 3.  Before you start taking shortcuts, see if it really matters. Neither the time nor the memory for the explicit implementation usually matters

TESTABILITY TIPS�5. Design Guidelines

• 4. Take shortcuts by making things implicit only as you must to make significant reductions in time or space and only if you can show that such savings matter in the context of the whole system.

After all, doubling the speed of your implementation may mean nothing if all you’ve done is shaved 100 microseconds from a 500-millisecond process. The order in which you should make things implicit are: output encoding, input encoding, state code, state-symbol product, output table, transition table, state storage. That’s the order from least to most dangerous.

• 6.  Consider a hierarchical design if you have more than a few dozen states.
• 7.  Build, buy, or implement tools and languages that implement finite-state machines as software if you’re doing more than a dozen states routinely.
• 8.  Build in the means to initialize to any arbitrary state. Build in the transition verification instrumentation (the coverage analyzer). These are much easier to do with an explicit machine.

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Important

• 1. The behavior of a finite state machine is invariant under all encodings. Justify? (16 M)**
• 2. Write testers comments about state graphs (8 M)**
• 3. What are the types of bugs that can cause state graphs? (8 M)*
• 4. What are the principles of state testing. Discuss advantages and disadvantages. (8 M)
• 5. Write the design guidelines for building finite state machine into code. (8 M)
• 6. What are the software implementation issues in state testing? (8 M)
• 7. Explain about good state and bad state graphs. (8 M)
• 8. Explain with an example how to convert specification into state-graph. Also discuss how contradictions can come out. (16 M)
• 9. Write short notes on: (16 M)
• i. Transition Bugs
• ii. Dead States
• iii. State Bugs
• iv. Encoding Bugs

UNIT 8—GRAPH MATRICES AND APPLICATIONS

To be continue……………..