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A Quadratic Lower Bound for Simulation

Jan Friso Groote, Jan Martens

Abstract

We show that deciding simulation equivalence and simulation preorder have quadratic lower bounds assuming that the Strong Exponential Time Hypothesis holds. This is in line with the best know quadratic upper bounds of simulation equivalence. This means that deciding simulation is inherently quadratic. A typical consequence of this result is that computing simulation equivalence is fundamentally harder than bisimilarity.

A Quadratic Lower Bound for Simulation

Abstract

We show that deciding simulation equivalence and simulation preorder have quadratic lower bounds assuming that the Strong Exponential Time Hypothesis holds. This is in line with the best know quadratic upper bounds of simulation equivalence. This means that deciding simulation is inherently quadratic. A typical consequence of this result is that computing simulation equivalence is fundamentally harder than bisimilarity.

Paper Structure

This paper contains 3 sections, 1 theorem, 6 equations, 1 figure.

Table of Contents

  1. Introduction
  2. SETH implies that DFA-NEI has quadratic complexity
  3. SETH implies simulation has quadratic complexity

Key Result

Theorem 3

wehar2017complexity If $2$-DFA-NEI can be solved in $O(n^{2-\epsilon})$ for some constant $\epsilon >0$, then SETH is false.

Figures (1)

  • Figure 1: Automata accepting $L^\Psi_1$ (left), and $L^\Psi_2$ (right) for $\Psi=(x_1 \vee \overline{x_2}) \wedge (\overline{x_1} \vee x_2)$.

Theorems & Definitions (5)

  • Definition 1
  • Definition 2
  • Theorem 3
  • Definition 4
  • Definition 5