针对有限和无限格点，已存在可在二次时间复杂度内检测元胞自动机（CA）可逆性的算法。然而，我们能否在常数时间内识别出一种 $d$-状态的CA规则，使其对任意格点尺寸 $n\in \mathbb{N}$ 均保持可逆？为解决此问题，本文研究了在零边界条件下，一类一维、三邻域、$d$-状态有限元胞自动机（CAs）——即一阶元胞自动机（FDCAs）——在任意细胞数 $n\in \mathbb{N}$ 下的可逆性特性。在一阶元胞自动机（FDCA）中，局部规则由八个参数定义。为确保 $d$-状态 FDCA 的全局转移函数对任意细胞数 $n\in \mathbb{N}$ 均可逆，只需验证参数值之间的三个代数条件即可。基于这些条件，对于任意给定的 $d$，均可合成所有可逆的 FDCAs 规则；同样地，对于给定的 FDCA 规则，可通过检查这三个条件在常数时间内判定其可逆性。

There exists algorithms to detect reversibility of cellular automaton (CA) for both finite and infinite lattices taking quadratic time. But, can we identify a $d$-state CA rule in constant time that is always reversible for every lattice size $n\in \mathbb{N}$? To address this issue, this paper explores the reversibility properties of a subset of one-dimensional, $3$-neighborhood, $d$-state finite cellular automata (CAs), known as the first degree cellular automata (FDCAs) for any number of cells $(n\in \mathbb{N})$ under the null boundary condition. {In a first degree cellular automaton (FDCA), the local rule is defined using eight parameters. To ensure that the global transition function of $d$-state FDCA is reversible for any number of cells $(n\in \mathbb{N})$, it is necessary and sufficient to verify only three algebraic conditions among the parameter values. Based on these conditions, for any given $d$, one can synthesize all reversible FDCAs rules. Similarly, given a FDCA rule, one can check these conditions to decide its reversibility in constant time.