Linear logic by levels and bounded time complexity

@article{Baillot2010LinearLB,
  title={Linear logic by levels and bounded time complexity},
  author={P. Baillot and D. Mazza},
  journal={Theor. Comput. Sci.},
  year={2010},
  volume={411},
  pages={470-503}
}
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… Expand
30 Citations
Strong polynomial bound for light linear logic by levels
  • Highly Influenced
  • PDF
Polynomial Time Calculi
  • 3
  • PDF
Paths-based criteria and application to linear logic subsystems characterizing polynomial time
  • PDF
On Paths-Based Criteria for Polynomial Time Complexity in Proof-Nets
  • 3
  • PDF
Algebras and coalgebras in the light affine Lambda calculus
  • 2
  • Highly Influenced
  • PDF
An abstract approach to stratification in linear logic
  • 2
  • PDF
...
1
2
3
...

References

SHOWING 1-10 OF 53 REFERENCES
Light Linear Logic
  • J. Girard
  • Computer Science, Mathematics
  • Inf. Comput.
  • 1998
  • 251
  • PDF
Linear logic and polynomial time
  • D. Mazza
  • Mathematics, Computer Science
  • Mathematical Structures in Computer Science
  • 2006
  • 18
Light Logics and Optimal Reduction: Completeness and Complexity
  • 17
  • PDF
Stratified Bounded Affine Logic for Logarithmic Space
  • Ulrich Schöpp
  • Mathematics, Computer Science
  • 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)
  • 2007
  • 27
  • PDF
Light logics and optimal reduction: Completeness and complexity
  • 14
A logical account of pspace
  • 44
  • PDF
Light types for polynomial time computation in lambda-calculus
  • P. Baillot, K. Terui
  • Mathematics, Computer Science
  • Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
  • 2004
  • 46
  • PDF
Light Affine Set Theory: A Naive Set Theory of Polynomial Time
  • K. Terui
  • Mathematics, Computer Science
  • Stud Logica
  • 2004
  • 37
  • PDF
Verification of Ptime Reducibility for system F Terms: Type Inference in Dual Light Affine Logic
  • 26
  • PDF
On the Computational Complexity of Cut-Elimination in Linear Logic
  • 51
  • PDF
...
1
2
3
4
5
...