The unrealizability of a specification is often due to the assumption that the behavior of the environment is unrestricted. In this paper, we present algorithms for synthesis in bounded environments, where the environment can only generate input sequences that are ultimately periodic words (lassos) with finite representations of bounded size. We provide automata-theoretic and symbolic approaches for solving this synthesis problem, and also study the synthesis of approximative implementations from unrealizable specifications. Such implementations may violate the specification in general, but are guaranteed to satisfy the specification on at least a specified portion of the bounded-size lassos. We evaluate the algorithms on different arbiter specifications.

中文翻译：

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综合实现无法实现的规格的近似实现

规范的无法实现通常是由于假设环境的行为不受限制。在本文中，我们提出了在有限环境中进行合成的算法，其中环境只能生成输入序列，这些输入序列最终是具有有限大小的有限表示形式的周期性单词（lasosos）。我们提供了自动机理论和符号方法来解决此综合问题，并且还研究了来自无法实现的规范的近似实现的综合。此类实现通常可能会违反规范，但是可以保证至少在有界套索的指定部分上满足规范。我们根据不同的仲裁器规格评估算法。