Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.20262 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- The class TotP consists of functions that count the number of all paths of a nondeterministic polynomial-time Turing machine. In this paper, we give a predicate based definition of TotP, analogous to a standard definition of #P. From a new characterization of TotP it follows that many well known #P problems belong to TotP, and TotP = #P if and only if P = NP. We show that TotP has several closure properties of #P and GapP, and also properties that are not known to hold for #P and GapP. We also prove that the closure of TotP under left composition with FP+ is equivalent to TotP = FP+ and P = PP, and give examples of FP+-functions such that if TotP is closed under composition with them, then it is closed under composition with FP+.