A Functional Language for Logarithmic Space

13 years 10 months ago

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Abstract. More than being just a tool for expressing algorithms, a welldesigned programming language allows the user to express her ideas eﬃciently. The design choices however eﬀect the eﬃciency of the algorithms written in the languages. It is therefore of importance to understand how such choices eﬀect the expressibility of programming languages. The paper pursues the very low complexity programs by presenting a ﬁrst-order function algebra BCε that captures exactly lf, the functions computable in logarithmic space. This gives insights into the expressiveness of recursion. Moreover, it can be useful for the automatic analysis of programs’ resource usage and the separation of complexity classes. The important technical features of BCε are (1) a separation of variables into safe and normal variables where recursion can only be done over the latter; (2) linearity of the recursive call; and (3) recursion with a variable step length (course-of-value recursion). Unlike formula...

Peter Møller Neergaard

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