Program Complexity Using Hierarchical Abstract Computers

There is currently interest in measuring the complexity of a computer program with the evaluation of a program's control structure via its flowgraph representation. 1,2 How~ ever, the inclusion of the effects of data on these measures is often lacking. This paper proposes a new measure of program complexity that attempts to identify regions of lo~ cality by combining a contro~ structure approach with infor~ mation about data usage to get a valid measure of overall program complexity. The need for objective measures of program structure is important if the area of programming language design and implementation is to take on a more formal basis from the ad hoc techniques currently used. This work is related to that of Hellerman,3 Savage,4.5 and Chaitin in that the complexity of an algorithm is defined as the number of bits in the algorithm's representation, i.e., the number of bits in a program implementing the algorithm. A program implementing a given algorithm is considered to be better than another program implementing the same al~ gorithm if it has fewer bits in its representation. In order to provide a standardized representation for algorithms, the concept of a Hierarchical Abstract Computer is defined (HAC). Based on a primitive~level HAC, hierarchical levels of HAC modules are used to specify the structures and sequences of a specific algorithm. The modules are chosen according to the concept of a Prime Program Parse, 7 which defines a particular, unique sequence of subroutine decom~ positions from an original flowgraph representation of an