Theoretical Computer Science
Lambda calculus characterizations of poly-time
Fundamenta Informaticae - Special issue: lambda calculus and type theory
Information and Computation
The Expressiveness of Simple and Second-Order Type Structures
Journal of the ACM (JACM)
Intuitionistic Light Affine Logic
ACM Transactions on Computational Logic (TOCL)
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Linear types and non-size-increasing polynomial time computation
Information and Computation - Special issue: ICC '99
Soft linear logic and polynomial time
Theoretical Computer Science - Implicit computational complexity
On an interpretation of safe recursion in light affine logic
Theoretical Computer Science - Implicit computational complexity
The intensional content of Rice's theorem
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Predicative analysis of feasibility and diagonalization
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
Light logics and optimal reduction: Completeness and complexity
Information and Computation
Elementary linear logic revisited for polynomial time and an exponential time hierarchy
APLAS'11 Proceedings of the 9th Asian conference on Programming Languages and Systems
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Light affine logic is a variant of linear logic with a polynomial cut-elimination procedure. We study the extensional expressive power of light affine logic with respect to a general notion of encoding of functions in the setting of the Curry–Howard correspondence. We consider light affine logic with both fixpoints of formulae and second-order quantifiers, and analyse the properties of polytime soundness and polytime completeness for various fragments of this system. In particular, we show that the implicative propositional fragment is not polytime complete if we place some reasonable conditions on the encodings. Following previous work, we show that second order leads to polytime unsoundness. We then introduce simple constraints on second-order quantification and fixpoints, and prove that the fragments obtained are polytime sound and complete.