Problem
Research questions and friction points this paper is trying to address.
Function Classification
Computational Complexity
BFF Class
Complete and tractable machine-independent characterizations of second-order polytime
🤖 AI Summary
A machine-independent, statically decidable characterization of second-order polynomial-time computable functions (BFF) has long remained an open challenge in higher-order computational complexity theory.
Method: We introduce the first sound, complete, and statically decidable characterization of second-order polytime, built upon second-order linear logic, a safety-type system, and a restricted recursion operator—yielding a computation-model-agnostic complexity semantics.
Contribution/Results: Our framework provides both completeness (all BFFs are captured) and decidability (membership is statically verifiable), resolving the longstanding quest for a uniform, model-free foundation. Unlike prior approaches tied to Turing machines or RAM models, our characterization is inherently syntactic and type-based, enabling static verification of higher-order polynomial-time boundedness. It establishes a general, reliable formal basis for efficient higher-order computability, advancing the logical foundations of implicit computational complexity.
Innovation
Methods, ideas, or system contributions that make the work stand out.
BFFs characterization
polynomial-time computability
two-step classification method
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