The descriptional complexity of basic operations on regular languages using 1-limited automata, a restricted version of one-tape Turing machines, is investigated. When simulating operations on deterministic finite automata with deterministic 1-limited automata, the sizes of the resulting devices are polynomial in the sizes of the simulated machines. The situation is different when the operations are applied to deterministic 1-limited automata: while for boolean operations the simulations remain polynomial, for product, star, and reversal they cost exponential in size. The costs for product and star do not reduce if the given machines are sweeping two-way deterministic finite automata. These bounds are tight.

研究了使用 1 有限自动机（单带图灵机的受限版本）对常规语言进行基本操作的描述复杂性。当使用确定性 1 有限自动机模拟确定性有限自动机上的操作时，所得设备的大小是模拟机器大小的多项式。当运算应用于确定性 1 有限自动机时，情况有所不同：对于布尔运算，模拟仍然是多项式，而对于乘积、星形和反转，它们的成本是指数级的。如果给定的机器正在扫除双向确定性有限自动机，则产品和明星的成本不会减少。这些界限很严格。