Related papers: Church => Scott = Ptime: an application of resourc…

We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class $\operatorname{PTIME}$ of languages computable in polynomial time in terms of differential…

We combine dependent types with linear type systems that soundly and completely capture polynomial time computation. We explore two systems for capturing polynomial time: one system that disallows construction of iterable data, and one,…

The outcomes of this paper are twofold. Implicit complexity. We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class PTIME of languages computable in…

Soft linear logic ([Lafont02]) is a subsystem of linear logic characterizing the class PTIME. We introduce Soft lambda-calculus as a calculus typable in the intuitionistic and affine variant of this logic. We prove that the (untyped) terms…

This paper introduces a more restrictive notion of feasibility of functionals on Baire space than the established one from second-order complexity theory. Thereby making it possible to consider functions on the natural numbers as running…

In a previous work Baillot and Terui introduced Dual light affine logic (DLAL) as a variant of Light linear logic suitable for guaranteeing complexity properties on lambda calculus terms: all typable terms can be evaluated in polynomial…

This paper provides an alternate characterization of type-two polynomial-time computability, with the goal of making second-order complexity theory more approachable. We rely on the usual oracle machines to model programs with subroutine…

In a previous work we introduced Dual Light Affine Logic (DLAL) ([BaillotTerui04]) as a variant of Light Linear Logic suitable for guaranteeing complexity properties on lambda-calculus terms: all typable terms can be evaluated in polynomial…

There is a subset of computational problems that are computable in polynomial time for which an existing algorithm may not complete due to a lack of high performance technology on a mission field. We define a subclass of deterministic…

The present article introduces ptarithmetic (short for "polynomial time arithmetic") -- a formal number theory similar to the well known Peano arithmetic, but based on the recently born computability logic (see…

We give two natural definitions of polynomial-time computability for L2 functions; and we show them incomparable (unless complexity class FP_1 includes #P_1).

"Clarithmetic" is a generic name for formal number theories similar to Peano arithmetic, but based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html) instead of the more traditional classical or intuitionistic logics.…

We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by…

The Church-Turing thesis asserts that if a partial strings-to-strings function is effectively computable then it is computable by a Turing machine. In the 1930s, when Church and Turing worked on their versions of the thesis, there was a…

A famous result due to Ko and Friedman (1982) asserts that the problems of integration and maximisation of a univariate real function are computationally hard in a well-defined sense. Yet, both functionals are routinely computed at great…

The earlier paper "Introduction to clarithmetic I" constructed an axiomatic system of arithmetic based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html), and proved its soundness and extensional completeness with respect…

We propose to use Church encodings in typed lambda-calculi as the basis for an automata-theoretic counterpart of implicit computational complexity, in the same way that monadic second-order logic provides a counterpart to descriptive…

Introduced by Dal Lago and Hofmann, quantitative realizability is a technique used to define models for logics based on Multiplicative Linear Logic. A particularity is that functions are interpreted as bounded time computable functions. It…

We introduce Church, a universal language for describing stochastic generative processes. Church is based on the Lisp model of lambda calculus, containing a pure Lisp as its deterministic subset. The semantics of Church is defined in terms…

The field of implicit complexity has recently produced several bounded-complexity programming languages. This kind of language allows to implement exactly the functions belonging to a certain complexity class. We here present a…