Theoretical Computer Science
Lambda calculus characterizations of poly-time
Fundamenta Informaticae - Special issue: lambda calculus and type theory
On the fine structure of the exponential rule
Proceedings of the workshop on Advances in linear logic
Information and Computation
Intuitionistic Light Affine Logic
ACM Transactions on Computational Logic (TOCL)
Linear types and non-size-increasing polynomial time computation
Information and Computation - Special issue: ICC '99
On an interpretation of safe recursion in light affine logic
Theoretical Computer Science - Implicit computational complexity
Context Semantics, Linear Logic and Computational Complexity
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
A local criterion for polynomial-time stratified computations
FOPARA'09 Proceedings of the First international conference on Foundational and practical aspects of resource analysis
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We introduce a multimodal stratified framework MS that generalizes an idea hidden in the definitions of Light Linear/Affine logical systems: "More modalities means more expressiveness". MS is a set of building-rule schemes that depend on parameters. We interpret the values of the parameters as modalities. Fixing the parameters yields deductive systems as instances of MS, that we call subsystems . Every subsystem generates stratified proof nets whose normalization preserves stratification , a structural property of nodes and edges, like in Light Linear/Affine logical systems. A first result is a sufficient condition for determining when a subsystem is strongly polynomial time sound. A second one shows that the ability to choose which modalities are used and how can be rewarding. We give a family of subsystems as complex as Multiplicative Linear Logic -- they are linear time and space sound -- that can represent Church numerals and some common combinators on them.