有限交互系统的不可判定性结果
Undecidability Results for Finite Interactive Systems
摘要：
最近提出了一种新的方法来设计大规模并行和交互式程序设计语言，使用RV系统（交互式系统与寄存器和语音）和Agapia编程。在本文中，我们提出了一些理论结果FIS（有限交互系统），用于指定这些系统中的控制和相互作用的基本机制。首先，我们给出了一个证明的不可判定性的空虚问题的FIS，通过减少后对应问题。接下来，我们使用这个证明中的构造来得到其他不可判定性结果，例如，对于FIS中的过渡的可访问性，或者对于FIS所识别的语言的有限性。最后，我们提出了一个简单的证明FIS和瓷砖系统之间的等价性，明确表示，他们精确地捕捉可识别的二维语言。
英文摘要：
A new approach to the design of massively parallel and interactive programming languages has been recently proposed using rv-systems (interactive systems with registers and voices) and Agapia programming. In this paper we present a few theoretical results on FISs (finite interactive systems), the underlying mechanism used for specifying control and interaction in these systems. First, we give a proof for the undecidability of the emptiness problem for FISs, by reduction to the Post Correspondence Problem. Next, we use the construction in this proof to get other undecidability results, e.g., for the accessibility of a transition in a FIS, or for the finiteness of the language recognized by a FIS. Finally, we present a simple proof of the equivalence between FISs and tile systems, making explicit that they precisely capture recognizable two-dimensional languages.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
