2025/04/28 by Yaroslav Ivanashev, Ivanashev, Yaroslav
Computer Science · #Computational Complexity (cs.CC) #FOS: Computer and information sciences #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2504.20262
openalex publication_date 2025/04/28 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28
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+.