Machine models and simulations
Handbook of theoretical computer science (vol. A)
A logical calculus for polynomial-time realizability
Methods of Logic in Computer Science
Information and Computation
Dependent types in practical programming
Proceedings of the 26th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Intuitionistic Light Affine Logic
ACM Transactions on Computational Logic (TOCL)
Linear Types and Non Size-Increasing Polynomial Time Computation
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Realizability models for BLL-like languages
Theoretical Computer Science - Implicit computational complexity
Soft linear logic and polynomial time
Theoretical Computer Science - Implicit computational complexity
Typing lambda terms in elementary logic with linear constraints
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
The weak lambda calculus as a reasonable machine
Theoretical Computer Science
Multiplexor Categories and Models of Soft Linear Logic
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Light types for polynomial time computation in lambda calculus
Information and Computation
A semantic proof of polytime soundness of light affine logic
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
A Categorical Setting for Lower Complexity
Electronic Notes in Theoretical Computer Science (ENTCS)
Light logics and optimal reduction: Completeness and complexity
Information and Computation
Realizability models and implicit complexity
Theoretical Computer Science
An invariant cost model for the lambda calculus
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Space-Efficient computation by interaction
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
| Hi-index | 0.00 |
We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by one of us), Light Affine Logic and Soft Affine Logic. The proofs are based on a common semantical framework which is merely instantiated in four different ways. The framework consists of an innovative modification of realizability which allows us to use resource-bounded computations as realisers as opposed to including all Turing computable functions as is usually the case in realizability constructions. For example, all realisers in the model for LFPL are polynomially bounded computations whence soundness holds by construction of the model. The work then lies in being able to interpret all the required constructs in the model. While being the first entirely semantical proof of polytime soundness for light logics, our proof also provides a notable simplification of the original already semantical proof of polytime soundness for LFPL. A new result made possible by the semantic framework is the addition of polymorphism and a modality to LFPL thus allowing for an internal definition of inductive datatypes.