ISBN : 978-81-963532-2-3 (E-Book) 1 2 ProgramVolume The length of a program (i.e. the total number of operators and operands used in the code)dependsonthechoiceoftheoperatorsandoperandsused.Inotherwords,forthesameprogramming problem,thelengthwoulddependontheprogrammingstyle.Thistypeofdependency would produce different measures of length for essentially the same problem whendifferentprogramminglanguagesareused.Thus,whileexpressingprogramsize,theprogramming languageused must be taken intoconsideration: V =Nlogη 2 Here the program volume V is the minimum number of bits needed to encode the program. Infact,torepresentηdifferentidentifiersuniquely,atleastlogηbits(whereηistheprogram 2 vocabulary)willbeneeded.Inthisscheme,Nlogηbitswillbeneededtostoreaprogramof 2 lengthN.Therefore,thevolumeVrepresentsthesizeoftheprogrambyapproximatelycompensatingfort heeffect of theprogramminglanguageused. PotentialMinimumVolume The potential minimum volume V* is defined as the volume of most succinct program in which aproblem can be coded. The minimum volume is obtained when the program can be expressedusing a single source code instruction. say a function call like foo( ) ;. In other words, the volumeis bound from below due to the fact that a program would have at least two operators and no lessthantherequisite numberof operands. Thus,ifanalgorithmoperatesoninputandoutputdatad,d,…d,themostsuccinctprogram wouldbef(d, d, … d);forwhich η=2, η=n. Therefore,V*=(2+η)log(2+η). 1 2 1 2 n 1 2 n 2 2 2 The program level L is given by L = V*/V. The concept of program level L is introduced in anattempt to measure the level of abstraction provided by the programming language. Using thisdefinition,languages canberanked into levels thatalso appear intuitivelycorrect. The above result implies that the higher the level of a language, the less effort it takes to 157 Software Engineering Keerthana P, Manasa KN, Ganga D Bengal
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