Theoretical Computer Science
Bounded linear logic: a modular approach to polynomial-time computability
Theoretical Computer Science
Lambda calculus characterizations of poly-time
Fundamenta Informaticae - Special issue: lambda calculus and type theory
A new recursion-theoretic characterization of the polytime functions
Computational Complexity
A foundational delineation of poly-time
Papers presented at the IEEE symposium on Logic in computer science
Proof-nets and the Hilbert space
Proceedings of the workshop on Advances in linear logic
Information and Computation
Intuitionistic Light Affine Logic
ACM Transactions on Computational Logic (TOCL)
Additives of linear logic and normalization: part I: A (restricted) Church--Rosser property
Theoretical Computer Science - Linear logic
Linear logic and elementary time
Information and Computation - Special issue: ICC '99
Stratified coherence spaces: a denotational semantics for light linear logic
Theoretical Computer Science - Implicit computational complexity
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
Light Types for Polynomial Time Computation in Lambda-Calculus
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Optimizing optimal reduction: A type inference algorithm for elementary affine logic
ACM Transactions on Computational Logic (TOCL)
Obsessional Cliques: A Semantic Characterization of Bounded Time Complexity
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Linear logic and polynomial time
Mathematical Structures in Computer Science
Stratified Bounded Affine Logic for Logarithmic Space
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
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
A soft type assignment system for &lambda-calculus
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
| Hi-index | 5.23 |
We give a new characterization of elementary and deterministic polynomial time computation in linear logic through the proofs-as-programs correspondence. Girard's seminal results, concerning elementary and light linear logic, achieve this characterization by enforcing a stratification principle on proofs, using the notion of depth in proof nets. Here, we propose a more general form of stratification, based on inducing levels in proof nets by means of indices, which allows us to extend Girard's systems while keeping the same complexity properties. In particular, it turns out that Girard's systems can be recovered by forcing depth and level to coincide. A consequence of the higher flexibility of levels with respect to depth is the absence of boxes for handling the paragraph modality. We use this fact to propose a variant of our polytime system in which the paragraph modality is only allowed on atoms, and which may thus serve as a basis for developing lambda-calculus type assignment systems with more efficient typing algorithms than existing ones.