Nonuniform families of polynomial-size quantum finite automata and quantum logarithmic-space computation with polynomial-size advice

The state complexity of a finite(-state) automaton intuitively measures the size description automaton. Sakoda and Sipser [STOC 1972, pp. 275–286] were concerned with nonuniform families finite automata they discussed behaviors classes defined by such having polynomial-size complexity. In similar fashion, we introduce using quantum empowered flexible use garbage tapes. We first present general inclusion separation relationships among various one-way automata, including deterministic, nondeterministic, probabilistic, polynomially many inner states. For two-way equipped tapes, show close relationship between family parameterized class induced logarithmic-space computation assisted advice. further establish direct connection space-bounded advice whose transitions are dictated superpositions transition tables.