Halstead's software science is an analytical estimation method that uses simple assumptions and program parameters like unique operators, unique operands, total operators, and total operands to estimate properties of a program like overall length, potential minimum volume, actual volume, effort required, and development time. It defines terms like program vocabulary, program length, program volume, potential program volume, program level, and uses equations involving these terms to estimate effort and length of a program based on the counts of unique operators and operands.

1. Halsted’s software scienceAn Analytical Technique
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PREPARED BY-
NUR ISLAM
Department of Information Technology
BESU, SHIBPUR

2. Halstead’s Software Science
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 Halstead’s software science is an analytical
estimation method.
-Have scientific basis
 Starts with few simple assumptions about the
product, Halstead used few primitive program parameters
to develop expressions for:
1.
2.
3.
4.
5.
Overall program length
Potential minimum volume and Program level
Actual volume
Effort
Development time

3. Important Keywords
3
 Operator in general: a symbol or function
representing a mathematical operation.







assignments arithmetic and logical operators
Parentheses pair, block begin/end pair
If…then… else… endif
Do…. While
Statement terminator “;”
Bitwise operator
Pointers operator

4. Important Keywords
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 Operands in general: A quantity to which an
operator is applied
– Subroutine declarations
– Variable declarations
– Variables and constants used with operators
in an expression

5. Example
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2.
1.
a=&b
• Operands: a , b
• Operators : = , &
3.
int func (int a, int b)
{
...
}
• Operators:
{} , (), “,”
func(a, b);
• Operators: func, “,” , “;”
, “()”
• Operands: a , b

6. Halstead’s Software Science
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• For any giving programs lets define the following
parameters:
– η1 be the number of unique parameters used in the
program
– η2 be the number of unique operands used in the
program
– N1 be the number of the total parameters used in the
program
– N2 be the number of the total operands used in the
program

7. Halstead’s Software Science
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 Length and Vocabulary:
– Program Length (N)= N1 + N2
This notation agrees with our understanding of the total
length of a program as the total count of tokens
(operators and operands)
– Program Vocabulary (η)= η1 + η2

8. Halstead’s Software Science
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 Program Volume:
Program volume (V)= is the minimum number of bits needed
to encode the program
– Program vocabulary and length depends on the
programming style
– Different lengths of programs, corresponding to the same
problem when different languages are used
– We need to express the program length by taking the
programming language into consideration

9. Halstead’s Software Science
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Program volume (V)= is the minimum number of
bits needed to encode the program
– Program volume V = N log2(η)
• To represent η different tokens we need log2(η) bits
– Example: to represent 8 operands we need 3
bits
• For a program of N length, we need N log2(η) bits
– Program volume represents the size of the program
by approximately compensating the effect of the
programming language used

10. Halstead’s Software Science
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Potential Program Volume (V*):
– V* is the volume of the most concise program in which
the problem can be coded
– A program require at least 2 operators (η1=2) and the
required number of operands is η2
• Example : func()
– Therefore: V* = (2+η2) log2(2+η2)
– Program Level (L) = V*/V
– Program level gives an indication of the language level
of abstraction
– Higher L, higher the language is easier to program with
• Example: Assembly vs. C#

11. Halstead’s Software Science
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 Effort and Time:
– To obtain the needed effort , we divide the
program volume (size) on the program level
(complexity)
2
–Effort = E =V / L = V /V*
– The programmer’s time needed to finish the
program (T) = E / S, where S is the speed of mental
discriminations
• The recommended value of S is 18

12. Halstead’s Software Science
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 Estimation of Length:
•Although the program length can be estimated
easily using the previous discussed equation N =
N1+N2, this can be done before starting the
programming activities.
• Instead, we can calculate the length depending on
the unique numbers of operands and operators

13. Halstead’s Software Science
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• Halstead assumptions are based on:
– Program are unlikely to have several identical
parts that are greater than (η)
– Identical parts are usually made into procedures
and functions
– Any program of length N consists of N/η
unique strings (of length η)
r
– for an alphabet of size K, there are K strings of
length r

14. Halstead’s Software Science
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N = η1 log2 (η1) + η2log2(n2)
• Experimental evidence showed that the actual and
the computed values are very close
• Results may be inaccurate when dealing with small
programs or subsystems individually

15. Recap
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 Unique operators
 Unique Operands
 Total Operators
 Total Operands
 Program Vocabulary
 Program Length
 Program Volume
 Effort
 Time
 Estimated Length
 Estimated Effort
:
:
:
:
:
:
:
:
:
:
:
η1
η2
N1
N2
η=η1+η2
N=N1+N2
Nlog2η
E=V/L
T=E/S
N=η1log2η1+η2log2η2
E=V.(η1/η2).(N2/2)

16. Example
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Main()
{
int a, b, c, avg;
scanf(“%d %d %d”, &a, &b, &c);
avg = (a +b +c )/3;
printf(“avg = %d”, avg);
}

17. Example
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The unique operators are:
main, (), {}, int, scanf, &, “, ”, “;”, =, +, /, printf
The unique operands are:
a, b, c, &a, &b, &c, a +b +c, avg, 3,
“%d %d %d”, “avg = %d”
therefore η1 = 12, η2 = 11
N
= 12 log2(12)+ 11log2(11)
=81
V
= Nlog2(η) = 81log2(23)
= 366

18. Resources
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• Wikipedia
• Fundamentals of Software Engineering by
Rajib Mall, Chapter 3

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