Some Observations Concerning Formal Differentiation of Set Theoretic Expressions

Cover Some Observations Concerning Formal Differentiation of Set Theoretic Expressions
Some Observations Concerning Formal Differentiation of Set Theoretic Expressions
M Sharir
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i n jl eie it a t ion js descriaed in IPs]*) As aeueloped by these authors formal- differentiation turns out to be a powerfjl mecnaiisn for i u^r jve-aerit Tf i very h i ih level version of an alcorithm. Its application C3n produce a new version of an algorithm that runs an order of majnicude faster than its original versicr-. These two properties of formal differentiation* namely that on one hard it is capable of changing the asymptotic oehavior of a Lgori t hms » ard on the other hand that it... is nor^ r orn 1 I i z aole and systematic than many other proqrafT tr ansformat ion methods* makes this a technique c1 central research interest. ^in/ interestinq examples of algoriihni transformation or fornal differentiation are qiven in C^aJ.
The present paper contains three observations concerniPi; formal differentiation. The startini point of our first oose'*vat i on * which is cevelcped in section 2* is that as descrioed till now (e. G. Ir CPa])t formal differentiation tecnniques remain somewhat less methocical than their algebraic counterjarts jince they rely on larger collections of special rules.


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