2024/04/20 by Yamakami, Tomoyuki · 1 citation
#Computational Complexity (cs.CC) #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL)
paper · doi:10.48550/arxiv.2404.13254
Nonuniform families of polynomial-size finite automata and pushdown automata respectively have strong connections to nonuniform-NL and nonuniform-LOGCFL. We examine the behaviors of unambiguous and co-nondeterministic computations produced by such families of automata operating multiple counters, where a counter is a stack using only a single non-bottom symbol. As immediate consequences, we obtain various collapses of the complexity classes of families of promise problems solvable by finite and pushdown automata families when all valid instances are limited to either polynomially long strings or unary strings. A key technical ingredient of our proofs is an inductive counting of reachable vertices of each computation graph of finite and pushdown automata that operate multiple counters simultaneously.