{"title":"Decidability of multiset, set and numerically decipherable directed figure codes","authors":"Wlodzimierz Moczurad","doi":"10.23638/DMTCS-19-1-11","DOIUrl":null,"url":null,"abstract":"Codes with various kinds of decipherability, weaker than the usual unique\ndecipherability, have been studied since multiset decipherability was\nintroduced in mid-1980s. We consider decipherability of directed figure codes,\nwhere directed figures are defined as labelled polyominoes with designated\nstart and end points, equipped with catenation operation that may use a merging\nfunction to resolve possible conflicts. This is one of possible extensions\ngeneralizing words and variable-length codes to planar structures. Here,\nverification whether a given set is a code is no longer decidable in general.\nWe study the decidability status of figure codes depending on catenation type\n(with or without a merging function), decipherability kind (unique, multiset,\nset or numeric) and code geometry (several classes determined by relative\npositions of start and end points of figures). We give decidability or\nundecidability proofs in all but two cases that remain open.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discret. Math. Theor. Comput. Sci.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23638/DMTCS-19-1-11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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.