The aim of this work is to thoroughly investigate Buchi automata augmented with spatial constraints. The input trees of such an automaton are infinite k-ary Sigma-trees, with the nodes standing for time points, and Sigma including, additionally to its uses in classical k-ary Sigma-trees, the description of the snapshot of an n-object spatial scene of interest. The constraints, from an RCC8-like spatial Relation Algebra (RA) x, are used to impose spatial constraints on objects of the spatial scene, eventually at different nodes of the input trees. We show that a Buchi alternating automaton augmented with spatial constraints can be simulated with a classical Buchi nondeterministic automaton of the same type, augmented with spatial constraints. We then provide a nondeterministic doubly depth-first polynomial space algorithm for the emptiness problem of the latter automaton. Our main motivation came from another work, also submitted to this conference, which defines a spatio-temporalisation of the well-known family ALC(D) of description logics with a concrete domain: together, the two works provide an effective solution to the satisfiability problem of a concept of the spatio-temporalisation with respect to a weakly cyclic TBox.

中文翻译：

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Buchi 自动机增加了空间约束：模拟具有不确定性的交替并确定后者的空性问题

这项工作的目的是彻底研究增强空间约束的 Buchi 自动机。这种自动机的输入树是无限的 k 元 Sigma 树，节点代表时间点，而 Sigma 除了在经典 k 元 Sigma 树中的使用外，还包括对 n-元快照的描述。感兴趣的对象空间场景。来自类似 RCC8 的空间关系代数 (RA) x 的约束用于对空间场景的对象施加空间约束，最终在输入树的不同节点上。我们表明，可以用相同类型的经典 Buchi 非确定性自动机模拟增强空间约束的 Buchi 交替自动机，增强空间约束。然后，我们为后一个自动机的空性问题提供了一种非确定性双深度优先多项式空间算法。我们的主要动机来自另一项工作，也提交给本次会议，该工作定义了具有具体领域的描述逻辑的著名家族 ALC(D) 的时空化：这两项工作共同为可满足性提供了有效的解决方案关于弱循环 TBox 的时空化概念的问题。