On Basic Feasible Functionals and the Interpretation Method - Symbolic analysis and Component-based design for Modular Real-Time Embedded Systems
Communication Dans Un Congrès Année : 2024

On Basic Feasible Functionals and the Interpretation Method

Résumé

The class of basic feasible functionals (BFF) is the analog of FP (polynomial time functions) for type-2 functionals, that is, functionals that can take (first-order) functions as arguments. BFF can be defined through Oracle Turing machines with running time bounded by second-order polynomials. On the other hand, higher-order term rewriting provides an elegant formalism for expressing higher-order computation. We address the problem of characterizing BFF by higher-order term rewriting. Various kinds of interpretations for first-order term rewriting have been introduced in the literature for proving termination and characterizing (first-order) complexity classes. In this paper, we consider a recently introduced notion of cost–size interpretations for higher-order term rewriting and see definitions as ways of computing functionals. We then prove that the class of functionals represented by higher-order terms admitting a certain kind of cost–size interpretation is exactly BFF.
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hal-04743265 , version 1 (18-10-2024)

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Patrick Baillot, Ugo Dal Lago, Cynthia Kop, Deivid Vale. On Basic Feasible Functionals and the Interpretation Method. FoSSaCS 2024 - 27th International Conference on Foundations of Software Science and Computation Structures, Apr 2024, Luxembourg, Luxembourg. pp.70-91, ⟨10.1007/978-3-031-57231-9_4⟩. ⟨hal-04743265⟩
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