On the Expressive Power of Light Affine Logic
نویسنده
چکیده
Light affine logic (LAL) is a formal system derived from linear logic that is claimed to correspond, through the Curry-Howard Isomorphism, to the class PTIME of polytime functions. The completeness of the system with respect to PTIME has been proven by embedding different presentations of PTIME into LAL. The dual property of polytime soundness, on the other hand, has been stated and proven in a more debatable way, depending crucially on the underlying coding scheme. In this paper, we introduce two relevant classes of coding schemes, namely uniform and canonical coding schemes. We then investigate on the equality between PTIME and the classes of functions that are representable in LAL using these coding schemes, obtaining a positive and a negative result.
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