Halstead’s Software Science

Halstead’s  Software  Science:

Statement:

A computer program is an implementation of an algorithm considered to be a collection of tokens which can be classified as either operators or operand.

• All software science metrics can be defined in terms of these basic symbols. These symbols are called as a token.
• The basic measures are
  • n1 = count of unique operators.
  • n2 = count of unique operands.
  • N1 = count of total occurrences of operators.
  • N2 = count of total occurrence of operands.
  • Size of the program can be expressed as N = N1 + N2.
• Program Volume (V)

The unit of measurement of volume is the standard unit for size "bits." It is the actual size of a program if a uniform binary encoding for the vocabulary is used.        V=N*log2n

• Program Level (L)

The value of L ranges between zero and one, with L=1 representing a program written at the highest possible level (i.e., with minimum size).

        L=V*/V

• Program Difficulty

The difficulty level or error-proneness (D) of the program is proportional to the number of the unique operator in the program.D= (n1/2) * (N2/n2)

• Programming Effort (E)

The unit of measurement of E is elementary mental discriminations.

    E=V/L=D*V

• Estimated Program Length

According to Halstead, The first Hypothesis of software science is that the length of a well-structured program is a function only of the number of unique operators and operands.  N=N1+N2.And estimated program length is denoted by N^

      N^ = n1log2n1 + n2log2n2

• Potential Minimum Volume

The potential minimum volume V* is defined as the volume of the most short program in which a problem can be coded.

     V* = (2 + n2*) * log2 (2 + n2*)

Here, n2* is the count of unique input and output parameters

• Size of Vocabulary (n)

The size of the vocabulary of a program, which consists of the number of unique tokens used to build a program, is defined as: n=n1+n2

Where n =vocabulary of a program

n1=number of unique operators

n2=number of unique operands

• Language Level - Shows the algorithm implementation program language level. The same algorithm demands additional effort if it is written in a low-level program language. For example, it is easier to program in Pascal than in Assembler.

        L' = V / D / D

lambda = L * V* = L2 * V

Advantages:

• Predicts error rate.
• Predicts maintenance effort
• Simple to calculate
• Measure overall quality
• Used for any language

Disadvantages:

• Depends on complete code
• Complexity increases as program level decreases
• Difficult to compute