✦ LIBER ✦

Achilles and the Tortoise Climbing Up the Arithmetical Hierarchy

✍ Scribed by Eugene Asarin; Oded Maler

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 653 KB
Volume: 57
Category: Article
ISSN: 0022-0000
DOI: 10.1006/jcss.1998.1601

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper we show how to construct for every set P of integers in the arithmetical hierarchy a dynamical system H with piecewise-constant derivatives such that deciding membership in P can be reduced to solving the reachability problem between two rational points for H. The ability of such apparently simple dynamical systems, whose definition involves only rational parameters, to ``solve'' highly unsolvable problems is closely related to Zeno's paradox, namely the ability to pack infinitely many discrete steps in a bounded interval of time. ] 1998 Academic Press

📜 SIMILAR VOLUMES

The Arithmetical Hierarchy of Real Numbe

The Arithmetical Hierarchy of Real Numbers

✍ Xizhong Zheng; Klaus Weihrauch 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 225 KB 👁 1 views

Bounded arithmetic and the polynomial hi

Bounded arithmetic and the polynomial hierarchy

✍ Jan Krajíček; Pavel Pudlák; Gaisi Takeuti 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 706 KB

Relating the bounded arithmetic and poly

Relating the bounded arithmetic and polynomial time hierarchies

✍ Samuel R. Buss 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 711 KB

A perspective of metabolic engineering s

A perspective of metabolic engineering strategies: moving up the systems hierarchy

✍ Thomas Bulter; Jeffrey R. Bernstein; James C. Liao 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 276 KB 👁 1 views

The theory of trying and goal-directed b

The theory of trying and goal-directed behavior: The effect of moving up the hierarchy of goals

✍ Darlene Bay; Harold Daniel 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 99 KB

## Abstract This article extends the literature regarding goal‐directed behavior as modeled by the theory of trying by incorporating the concept of the hierarchy of goals. Individuals develop “programs” intended to implement their principles and life goals. Within these programs, goals are arranged

Moving up the hierarchy: A hypothesis on

Moving up the hierarchy: A hypothesis on the evolution of a genetic sex determination pathway

✍ Adam S. Wilkins 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 744 KB

A hypothesis on the evolutionary origin of the genetic pathway of sex determination in the nematode Caenorhabditis elegans is presented here. It is suggested that the pathway arose in steps, driven by frequency-dependent selection for the minority sex at each step, and involving the sequential acqui