发表机构
Tampere University; University of Helsinki（坦佩雷大学; 赫尔辛基大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出循环事件自动机（RIAs）这一新自动机模型，通过分解双栈可见下推计算来识别图编码语言，并证明非确定性RIA语言对并、交、连接、Kleene星和反转封闭，确定性RIA对布尔运算封闭但空性不可判定。
AI 中文摘要
我们引入了循环事件自动机（RIAs），这是一种新的自动机模型，其动机源于对某些双栈可见下推计算的一种分解。该分解将顶点局部有限状态计算与连接连续顶点的循环单栈接口分离。该构造的动机源于对任意有序图的双栈可见下推编码，其字符串允许唯一分解为中心可折叠的顶点局部因子，且辅助栈在每个因子边界处为空。将每个因子折叠成一对符号的序列会产生局部接口变换。一个RIA由一个计算这些变换的有限状态单元和一个在连续因子间组合这些变换的循环层组成。RIAs不是操纵内部下推存储，而是将长距离栈存储器外部化为局部计算之间的循环接口。我们证明了非确定性RIA语言在并、交、连接、Kleene星号和反转运算下是封闭的。确定性RIAs在布尔运算下是封闭的，尽管空性判定仍然是不可判定的。
英文摘要
We introduce recurrent incidence automata (RIAs), a new automaton model motivated by a decomposition of certain two-stack visibly pushdown computations. The decomposition separates vertex-local finite-state computations from recurrent one-stack interfaces connecting consecutive vertices. The construction is motivated by a two-stack visibly pushdown encoding of arbitrary ordered graphs whose strings admit a unique factorization into center-foldable vertex-local factors and whose auxiliary stack is empty at every factor boundary. Folding each factor into a sequence of pair symbols yields a local interface transformation. An RIA consists of a finite-state unit that computes these transformations and a recurrent layer that composes them across consecutive factors. Rather than manipulating an internal pushdown store, RIAs externalize long-range stack memory into recurrent interfaces between local computations. We show that nondeterministic RIA languages are closed under union, intersection, concatenation, Kleene-*, and reversal. Deterministic RIAs are closed under Boolean operations, although emptiness remains undecidable.
CommentsIn Proceedings AFL 2026, arXiv:2608.23071
Journal refEPTCS 451, 2026, pp. 304-318
