Testing decipherability of directed figure codes with domino graphs

Various kinds of decipherability of codes, weaker than unique decipherability, have been studied since mid-1980s. We consider decipherability of directed gure codes, where directed gures are de ned as labelled polyomi- noes with designated start and end points, equipped with catenation operation that may use a merging function to resolve possible con icts. This setting ex- tends decipherability questions from words to 2D structures. In the present paper we develop a (variant of) domino graph that will allow us to decide some of the decipherability kinds by searching the graph for speci c paths. Thus the main result characterizes directed gure decipherability by graph properties

Note on Decipherability of Three-Word Codes

The theory of uniquely decipherable (UD) codes has been widely developed in connection with automata theory, combinatorics on words, formal languages, and monoid theory. Recently, the concepts of multiset decipherable (MSD) and set decipherable (SD) codes were developed to handle some special problems in the transmission of information. Unique decipherability is a vital requirement in a wide range of coding applications where distinct sequences of code words carry different information. However, in several applications, it is necessary or desirable to communicate a description of a sequence of events where the information of interest is the set of possible events, including multiplicity, but where the order of occurrences is irrelevant. Suitable codes for these communication purposes need not possess the UD property, but the weaker MSD property. In other applications, the information of interest may be the presence or absence of possible events. The SD property is adequate for such codes. Lempel (1986) showed that the UD and MSD properties coincide for two-word codes and conjectured that every three-word MSD code is a UD code. Guzmán (1995) showed that the UD, MSD, and SD properties coincide for two-word codes and conjectured that these properties coincide for three-word codes. In an earlier paper (2001), Blanchet-Sadri answered both conjectures positively for all three-word codes {c1,c2,c3} satisfying |c1| = |c2| = |c3|. In this note, we answer both conjectures positively for other special three-word codes. Our procedures are based on techniques related to dominoes

Multiset and Set Decipherable Codes

We extend some results of Lempel and Restivo on multiset decipherable codes to set decipherable codes

Monoids and Maximal Codes

In recent years codes that are not Uniquely Decipherable (UD) are been studied partitioning them in classes that localize the ambiguities of the code. A natural question is how we can extend the notion of maximality to codes that are not UD. In this paper we give an answer to this question. To do this we introduce a partial order in the set of submonoids of a monoid showing the existence, in this poset, of maximal elements that we call full monoids. Then a set of generators of a full monoid is, by definition, a maximal code. We show how this definition extends, in a natural way, the existing definition concerning UD codes and we find a characteristic property of a monoid generated by a maximal UD code.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Word Equations and Related Topics. Independence, Decidability and Characterizations

The three main topics of this work are independent systems and chains of word equations, parametric solutions of word equations on three unknowns, and unique decipherability in the monoid of regular languages. The most important result about independent systems is a new method giving an upper bound for their sizes in the case of three unknowns. The bound depends on the length of the shortest equation. This result has generalizations for decreasing chains and for more than three unknowns. The method also leads to shorter proofs and generalizations of some old results. Hmelevksii’s theorem states that every word equation on three unknowns has a parametric solution. We give a significantly simplified proof for this theorem. As a new result we estimate the lengths of parametric solutions and get a bound for the length of the minimal nontrivial solution and for the complexity of deciding whether such a solution exists. The unique decipherability problem asks whether given elements of some monoid form a code, that is, whether they satisfy a nontrivial equation. We give characterizations for when a collection of unary regular languages is a code. We also prove that it is undecidable whether a collection of binary regular languages is a code.Siirretty Doriast

Theatre Works' Desdemona: Fusing technology and tradition

“Interculturalism” needs to be expanded and redefined to include the responses of spectators as well as the work of artists. In what ways does Theatre Works' Desdemona, as seen at the 2000 Adelaide Festival, represent a “new wave of Asian production”? Or are such works disturbing evidence of the increasing erosion of the local

Testing decipherability of directed figure codes with domino graphs

Various kinds of decipherability of codes, weaker than unique de- cipherability, have been studied since mid-1980s. We consider decipherability of directed figure codes, where directed figures are defined as labelled polyomi- noes with designated start and end points, equipped with catenation operation that may use a merging function to resolve possible conflicts. This setting ex- tends decipherability questions from words to 2D structures. In the present paper we develop a (variant of) domino graph that will allow us to decide some of the decipherability kinds by searching the graph for specific paths. Thus the main result characterizes directed figure decipherability by graph properties