The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. An XCA is a one-dimensional cellular automaton which can dynamically create new cells between existing ones. The respective polynomial-time complexity class is shown to coincide with \({\le _{tt}^p}(\textsf {NP})\), that is, the class of decision problems polynomial-time truth-table reducible to problems in \(\textsf {NP}\). An alternative characterization based on a variant of non-deterministic Turing machines is also given. In addition, corollaries on select XCA variants are proven: XCAs with multiple accept and reject states are shown to be polynomial-time equivalent to the original XCA model. Finally, XCAs with alternative acceptance conditions are considered and classified in terms of \({\le _{tt}^p}(\textsf {NP})\) and the Turing machine polynomial-time class \(\textsf {P}\).

从复杂性理论的角度研究了细胞自动机的扩展细胞自动机（XCA）变体并对其进行了表征。XCA是一维元胞自动机，可以动态地在现有元胞之间创建新的元胞。各个多项式时间复杂度类别显示为与\（{\ le _ {tt} ^ p}（\ textsf {NP}）\）一致，即，决策问题的多项式时间真值表可简化为在问题\（\ textsf {NP} \）。还给出了基于不确定性图灵机变体的替代特征。此外，还证明了某些XCA变体的推论：具有多个接受和拒绝状态的XCA被证明是多项式时间，相当于原始XCA模型。最后，考虑具有替代接受条件的XCA，并根据\（{\ le _ {tt} ^ p}（\ textsf {NP}）\）和图灵机多项式时间类\（\ textsf {P} \）。