A tier-based typed programming language characterizing Feasible Functionals

The class of Basic Feasible Functionals BFF$_2$ is the type-2 counterpart of the class FP of type-1 functions computable in polynomial time. Several characterizations have been suggested in the literature, but none of these present a programming language with a type system guaranteeing this complexi...

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Bibliographic Details
Published in:	Logical methods in computer science Vol. 18, Issue 1; no. 1
Main Authors:	Hainry, Emmanuel, Kapron, Bruce M., Marion, Jean-Yves, Péchoux, Romain
Format:	Journal Article
Language:	English
Published:	Logical Methods in Computer Science Association 24.02.2022 Logical Methods in Computer Science e.V
Subjects:	Computation and Language Computer Science computer science - logic in computer science computer science - programming languages Logic in Computer Science
ISSN:	1860-5974, 1860-5974
Online Access:	Get full text
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Summary:	The class of Basic Feasible Functionals BFF$_2$ is the type-2 counterpart of the class FP of type-1 functions computable in polynomial time. Several characterizations have been suggested in the literature, but none of these present a programming language with a type system guaranteeing this complexity bound. We give a characterization of BFF$_2$ based on an imperative language with oracle calls using a tier-based type system whose inference is decidable. Such a characterization should make it possible to link higher-order complexity with programming theory. The low complexity (cubic in the size of the program) of the type inference algorithm contrasts with the intractability of the aforementioned methods and does not overly constrain the expressive power of the language.
ISSN:	1860-5974 1860-5974
DOI:	10.46298/lmcs-18(1:33)2022