标题： 关于人类语言编码最优性的类别及齐普夫定律的起源 显示英文标题

标题： On the class of coding optimality of human languages and the origins of Zipf's law

摘要： 这里我们提出了一种编码系统的新型最优性。该类的成员相对于最优编码线性偏移，因此表现出齐普夫定律，即频率排名的幂律分布。在该类中，齐普夫定律、规模-排名定律和规模-概率定律形成类似群的结构。我们识别出属于该类的人类语言。所有与齐普夫定律有足够一致性的语言都是该类的潜在成员。相反，其他物种的通信系统可能无法成为该类的成员，因为它们表现出指数分布，但海豚和座头鲸可能例外。我们提供了对双对数尺度下频率与排名图的新见解。对于任何系统，该尺度下的直线表明在非奇异编码和唯一可解编码下的最优码长度由一个斜率为齐普夫定律指数的线性函数偏移。对于在压缩下且被约束为唯一可解的系统，这样的直线可能表明该系统接近最优编码。我们提供了支持齐普夫定律起源于压缩的假设，并为压缩系统中齐普夫定律的出现定义了可测试条件。 显示英文摘要

摘要： Here we present a new class of optimality for coding systems. Members of that class are displaced linearly from optimal coding and thus exhibit Zipf's law, namely a power-law distribution of frequency ranks. Within that class, Zipf's law, the size-rank law and the size-probability law form a group-like structure. We identify human languages that are members of the class. All languages showing sufficient agreement with Zipf's law are potential members of the class. In contrast, there are communication systems in other species that cannot be members of that class for exhibiting an exponential distribution instead but dolphins and humpback whales might. We provide a new insight into plots of frequency versus rank in double logarithmic scale. For any system, a straight line in that scale indicates that the lengths of optimal codes under non-singular coding and under uniquely decodable encoding are displaced by a linear function whose slope is the exponent of Zipf's law. For systems under compression and constrained to be uniquely decodable, such a straight line may indicate that the system is coding close to optimality. We provide support for the hypothesis that Zipf's law originates from compression and define testable conditions for the emergence of Zipf's law in compressing systems.