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Implicit Computational Complexity: Part III

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If you have a question about this talk, please contact Anupam Das.

Implicit Computational Complexity (ICC) is a branch of computational complexity that aims at studying machine-free characterisations of complexity classes by means of languages or calculi that do not explicitly rely on time/space resource bounds, borrowing a variety of techniques and ideas from many areas of mathematical logic. ICC originates in the nineties from Bellantoni and Cook’s seminal paper introducing the algebra of functions “B” based on safe recursion and capturing the class of functions computable in polynomial time (FPTIME) [Bellantoni and Cook, 1992]. Roughly, safe recursion implements a form of “stratification” of data, whose role is to prevent computation overstepping a given resource bound.

In this talk I will start presenting Cobham’s notion of bounded recursion [Cobham, 1965], a forerunner of the machine-free approaches to complexity. Then, I will move on to Bellantoni and Cook’s algebra of functions B, sketching the proof of the characterisation theorem relating the functions definable in B and the functions in FPTIME . I will also mention how safe recursion and stratification can be scaled for capturing other major complexity classes. Finally, time allowing, I will present Hofmann’s SLR (Safe Linear Recursion) [Hofmann, 98], a type system implementing a higher-order formulation of safe recursion.

[NB: this is a physical-only whiteboard talk]

This talk is part of the Lab Lunch series.

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