Multiset and Set Decipherable Codes

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

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

Trees and graph packing

In this thesis we investigate two main topics, namely, suffix trees and graph packing problems. In Chapter 2, we present the suffix trees. The main result of this chapter is a lower bound on the size of simple suffix trees. In the rest of the thesis we deal with packing problems. In Chapter 3 we give almost tight conditions on a bipartite packing problem. In Chapter 4 we consider an embedding problem regarding degree sequences. In Chapter 5 we show the existence of bounded degree bipartite graphs with a small separator and large bandwidth and we prove that under certain conditions these graphs can be embedded into graphs with minimum degree slightly over n/2

A system for describing and deciding properties of regular languages using input altering transducers

ii, 94 leaves : ill. ; 29 cm.Includes abstract.Includes bibliographical references (leaves 92-94).We present a formal method for describing and deciding code related properties of regular languages using input altering transducers. We also provide an implementation of that method in the form of a web application. We introduce the concept of an input altering transducer. We show how to use such transducers to describe properties of languages and present examples of transducers describing some well known properties (like suffix codes, prefix codes, infix codes, solid codes, and others). We discuss some limitations of our method. In particular, all properties that can be described using input altering transducers are 3-independence properties. We also give an example of a 3-independence property that cannot be represented using a transducer. We explain how our method is a specialisation of a more general method based on language in-equations. We also discuss the relation between our method and a method that uses sets of trajectories to describe properties. In particular, we show how, for any given set of trajectories describing some property, to build an input altering transducer describing the same property. We introduce the concept of counterexample, which is a pair of words that, if a given language does not belong to a given property, illustrate that fact. We show how we can incorporate extracting such counterexample into our method. Finally, we provide some details on the implementation and usage of the web application that was built as a part of this research

Pragmatics of parallel suffix tree construction

Suffix trees are a well known data structure for facilitating a variety of queries on strings. Construction of the trees requires a considerable number of choices concerning the implementation. Several of those choices are examined in this paper. Performance studies are presented that reveal the consequences of these choices. The main focus of this paper is the implementation choices that influence suffix tree construction on parallel computers. Four algorithms are examined. Two are sequential and two are parallel. Results show that a sequential Algorithm developed by Edward McCreight generally has better performance than Alberto Apostolico's parallel algorithm on real machines. A streamlined version of Apostolico's algorithm helps parallel performance somewhat; but not enough to dethrone McCreight's design. The sequential naive algorithm studied gives a good simple reference point when understanding the other algorithms