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Decision Problems for Nonemptiness of Hyperlanguages: Undecidability and Complexity Results
Subject area: Science,Engineering and Technology · Area of research: Theoretical Computer Science
Abstract
This paper examines different choice issues connected with the nonemptiness of Non-Deterministic Limited Hyperautomata (NFH). I show that while the nonemptiness issue for NFH is for the most part undecidable, it becomes decidable for explicit pieces. I give a decrease from the Post Correspondence Issue (PCP) to demonstrate the undecidability of the nonemptiness issue for NFH, delineating how encoded arrangements of PCP can address legitimate hyperwords. Furthermore, I lay out that the nonemptiness issue for both NFH with existential and widespread evaluation (NFH? and NFH?) is NL-finished. At last, I present a choice methodology for the nonemptiness issue of NFH with blended evaluation (NFH??), demonstrating that it very well may be settled in polynomial space compared with the machine size. Our outcomes add to a more profound comprehension of hyperlanguage choice issues and their computational intricacy
How to cite this paper
@article{1707244,
author = {Hyacinthe Hamon},
title = {Decision Problems for Nonemptiness of Hyperlanguages: Undecidability and Complexity Results},
journal = {Iconic Research And Engineering Journals},
year = {2025},
volume = {8},
number = {8},
pages = {675-683},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1707244.pdf},
abstract = {This paper examines different choice issues connected with the nonemptiness of Non-Deterministic Limited Hyperautomata (NFH). I show that while the nonemptiness issue for NFH is for the most part undecidable, it becomes decidable for explicit pieces. I give a decrease from the Post Correspondence Issue (PCP) to demonstrate the undecidability of the nonemptiness issue for NFH, delineating how encoded arrangements of PCP can address legitimate hyperwords. Furthermore, I lay out that the nonemptiness issue for both NFH with existential and widespread evaluation (NFH? and NFH?) is NL-finished. At last, I present a choice methodology for the nonemptiness issue of NFH with blended evaluation (NFH??), demonstrating that it very well may be settled in polynomial space compared with the machine size. Our outcomes add to a more profound comprehension of hyperlanguage choice issues and their computational intricacy},
month = {February},
}