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Super Unique Tarski is in UEOPL

John Fearnley, Rahul Savani

Abstract

We define the Super-Unique-Tarski problem, which is a Tarski instance in which all slices are required to have a unique fixed point. We show that Super-Unique-Tarski lies in UEOPL under promise-preserving reductions.

Super Unique Tarski is in UEOPL

Abstract

We define the Super-Unique-Tarski problem, which is a Tarski instance in which all slices are required to have a unique fixed point. We show that Super-Unique-Tarski lies in UEOPL under promise-preserving reductions.

Paper Structure

This paper contains 9 sections, 7 theorems, 5 equations.

Table of Contents

  1. Introduction
  2. Definitions
  3. The Tarski fixed point problem.
  4. The Super-Unique-Tarski Problem
  5. Tarski instances with unique fixed points.
  6. The Super-Unique-Tarski problem.
  7. Super-Unique-Tarski is in UEOPL
  8. The reduction.
  9. Acknowledgement

Key Result

Theorem 1

Every monotone function on a complete lattice has a greatest and least fixed point.

Theorems & Definitions (13)

  • Theorem 1: Tarski55
  • Definition 2: Tarski
  • Theorem 3: Tarski55
  • Lemma 4: ChenLY23
  • proof
  • Lemma 5
  • proof
  • Definition 6: Super-Unique-Tarski
  • Definition 7: OPDC (FGMS20)
  • Lemma 8: FGMS20
  • ...and 3 more