Higher-order and symbolic computation: editorial

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Uniform Circuits & Boolean Proof Nets

21 pagesInternational audienceThe relationship between Boolean proof nets of multiplicative linear logic (APN) and Boolean circuits has been studied [Ter04] in a non-uniform setting. We refine this results by taking care of uniformity: the relationship can be expressed in term of the (Turing) polynomial hierarchy. We give a proofs-as-programs correspondence between proof nets and deterministic as well as non-deterministic Boolean circuits with a uniform depth-preserving simulation of each other. The Boolean proof nets class m&BN(poly) is built on multiplicative and additive linear logic with a polynomial amount of additive connectives as the non-deterministic circuit class NNC(poly) is with non-deterministic variables. We obtain uniform-APN = NC and m&BN(poly) = NNC(poly) = N

Scalable Certification for Typed Assembly Language

A type-based certifying compiler maps source code to machine code and target-level type annotations. The target-level annotations make it possible to prove easily that the machine code is type-safe, independent of the source code or compiler. To be useful across a range of source languages and compilers, the target-language type system should provide powerful type constructors for encoding higher-level invariants. Unfortunately, it is difficult..

Uniform circuits, & Boolean proof nets

The relationship between Boolean proof nets of multiplicative linear logic (APN) and Boolean circuits has been studied [Ter04] in a non-uniform setting. We refine the results taking care of uniformity: the relationship can be expressed in term of the (Turing) polynomial hierarchy. We give a proofs-as-programs correspondence between proof nets and deterministic as well as non-deterministic Boolean circuits with a uniform depth-preserving simulation of each other. The Boolean proof nets class m&BN(poly) is built on multiplicative and additive linear logic with a polynomial amount of additive connectives as the nondeterministic circuit class NNC(poly) is with non-deterministic variables. We obtain uniform-APN = NC and m&BN(poly) = NNC(poly) = NP