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2022•ComputabilityOpen access

Characterizing time computational complexity classes with polynomial differential equations

Riccardo Gozzi, Daniel S. Graça

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Abstract

In this paper we show that several classes of languages from computational complexity theory, such as [Formula: see text], can be characterized in a continuous manner by using only polynomial differential equations. This characterization applies not only to languages, but also to classes of functions, such as the classes defining the Grzegorczyk hierarchy, which implies an analog characterization of the class of elementary computable functions and the class of primitive recursive functions.

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What this paper is about

In this paper we show that several classes of languages from computational complexity theory, such as [Formula: see text], can be characterized in a continuous manner by using only polynomial differential equations. This characterization applies not only to languages, but also to classes of functions, such as the classes defining the Grzegorczyk hierarchy, which implies an analog characterization of the class of elementary computable functions and the class of primitive recursive functions.

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Available abstract

In this paper we show that several classes of languages from computational complexity theory, such as [Formula: see text], can be characterized in a continuous manner by using only polynomial differential equations. This characterization applies not only to languages, but also to classes of functions, such as the classes defining the Grzegorczyk hierarchy, which implies an analog characterization of the class of elementary computable functions and the class of primitive recursive functions.

Key concepts: Complexity class, PH, Structural complexity theory, EXPTIME, Hierarchy, Mathematics, Computational complexity theory, Characterization (materials science)

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