Theoretical Computer Science
Journal of the ACM (JACM)
Predicative Functional Recurrence and Poly-space
TAPSOFT '97 Proceedings of the 7th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
Ramified Recurrence and Computational Complexity II: Substitution and Poly-Space
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
Soft linear logic and polynomial time
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
A call-by-name lambda-calculus machine
Higher-Order and Symbolic Computation
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
Nondeterministic light logics and NP-time
TLCA'03 Proceedings of the 6th 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
The role of polymorphism in the characterisation of complexity by soft types
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
An Implicit Characterization of PSPACE
ACM Transactions on Computational Logic (TOCL)
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We describe some results inspired to Lafont's Soft Linear Logic (SLL) which is a subsystem of second-order linear logic with restricted rules for exponentials, correct and complete for polynomial time computations. SLL is the basis for the design of type assignment systems for lambda-calculus, characterizing the complexity classes PTIME, PSPACE and NPTIME. PTIME is characterized by a type assignments system where types are a proper subset of SLL formulae. The characterization consists in the fact that a well typed term can be reduced to normal form by a number of beta-reductions polynomial in its lenght, and moreover all polynomial time functions can be computed by well typed terms. PSPACE is characterized by a type assignment system obtained from the previous one, by extending the set of types by a type for booleans, and the lambda-calculus by two boolean constants and a conditional constructor. The system assigns types to terms in such a way that the evaluation of programs (closed terms of type boolean) can be performed carefully in polynomial space. Moreover all polynomial space decision problems can be computed by terms typable in this system. In order to characterize NPTIME we extend the lambda-calculus by a nondeterministic choice operator, and the system by a rule for dealing with this new term constructor.