Decidability of multiset, set and numerically decipherable directed figure codes

Wlodzimierz Moczurad
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引用次数: 4

Abstract

Codes with various kinds of decipherability, weaker than the usual unique decipherability, have been studied since multiset decipherability was introduced in mid-1980s. We consider decipherability of directed figure codes, where directed figures are defined as labelled polyominoes with designated start and end points, equipped with catenation operation that may use a merging function to resolve possible conflicts. This is one of possible extensions generalizing words and variable-length codes to planar structures. Here, verification whether a given set is a code is no longer decidable in general. We study the decidability status of figure codes depending on catenation type (with or without a merging function), decipherability kind (unique, multiset, set or numeric) and code geometry (several classes determined by relative positions of start and end points of figures). We give decidability or undecidability proofs in all but two cases that remain open.
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多集、集和数字可破译的有向图码的可判定性
自20世纪80年代中期多集可译码被引入以来,人们研究了比通常的唯一可译码能力更弱的各种可译码。我们考虑有向图代码的可解码性,其中有向图被定义为带有指定起点和终点的标记多线形,配备了可以使用合并函数来解决可能冲突的交错操作。这是将字和变长码推广到平面结构的一种可能的扩展。在这里,验证给定集合是否为码通常不再是可确定的。我们研究了图形码的可判定状态,这取决于串列类型(带或不带合并函数)、可判读类型(唯一、多集、集或数字)和码的几何形状(由图形起始点和结束点的相对位置决定的若干类)。除了两个悬而未决的案件外,我们在所有案件中都给出了可判性或不可判性的证明。
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