Theoretical Computer Science
Bounded linear logic: a modular approach to polynomial-time computability
Theoretical Computer Science
Linear logic: its syntax and semantics
Proceedings of the workshop on Advances in linear logic
Information and Computation
Intuitionistic Light Affine Logic
ACM Transactions on Computational Logic (TOCL)
A P-Time Completeness Proof for Light Logics
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Phase semantics for light linear logic
Theoretical Computer Science - Linear logic
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
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
Linear logic and polynomial time
Mathematical Structures in Computer Science
Verification of ptime reducibility for system f terms via dual light affine logic
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
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Starting from Girard's seminal paper on light linear logic (LLL), a number of works investigated on systems derived from linear logic to capture polynomial time computation within the computation-as-cut-elimination paradigm. The original syntax of LLL is too complicated, mainly because one has to deal with sequents which not just consist of formulas but also of `blocks' of formulas. We circumvent the complications of `blocks' by introducing a new modality $\nabla$ which is exclusively in charge of `additive blocks'. The most interesting feature of this purely multiplicative $\nabla$ is the possibility of the second-order encodings of additive connectives. The resulting system (with the traditional syntax), called Easy-LLL, is still powerful to represent any deterministic polynomial time computations in purely logical terms. Unlike the original LLL, Easy-LLL admits polynomial time strong normalization, namely, cut elimination terminates in a unique way in polytime by any choice of cut reduction strategies.