Enhanced string factoring from alphabet orderings

In this note we consider the concept of alphabet ordering in the context of string factoring. We propose a greedy-type algorithm which produces Lyndon factorizations with small numbers of factors along with a modification for large numbers of factors. For the technique we introduce the Exponent Parikh vector. Applications and research directions derived from circ-UMFFs are discussed.Comment: 9 page

Algorithms and Lower Bounds for Ordering Problems on Strings

This dissertation presents novel algorithms and conditional lower bounds for a collection of string and text-compression-related problems. These results are unified under the theme of ordering constraint satisfaction. Utilizing the connections to ordering constraint satisfaction, we provide hardness results and algorithms for the following: recognizing a type of labeled graph amenable to text-indexing known as Wheeler graphs, minimizing the number of maximal unary substrings occurring in the Burrows-Wheeler Transformation of a text, minimizing the number of factors occurring in the Lyndon factorization of a text, and finding an optimal reference string for relative Lempel-Ziv encoding

Deformations of colored sl(N) link homologies via foams

We generalize results of Lee, Gornik and Wu on the structure of deformed colored sl(N) link homologies to the case of non-generic deformations. To this end, we use foam technology to give a completely combinatorial construction of Wu's deformed colored sl(N) link homologies. By studying the underlying deformed higher representation theoretic structures and generalizing the Karoubi envelope approach of Bar-Natan and Morrison we explicitly compute the deformed invariants in terms of undeformed type A link homologies of lower rank and color.Comment: 64 pages, many figure

Bottom-up evaluation of HiLog in the context of deductive database systems

Bibliography: leaves 127-130.HiLog is a logic-based language which boasts the expressiveness of a higher-order syntax while retaining the simplicity of a first-order semantics. This work examines the suitability of Horn-clause HiLog as a query language for deductive databases by investigating the feasibility of adapting well-established Datalog evaluation algorithms for the evaluation of HiLog programs. Each of the evaluation algorithms examined in the work is formally described and verified in terms of completeness and correctness. Furthermore, a practical HiLog evaluator based on each algorithm verifies the feasibility of its implementation in a real-world context. It is demonstrated that the Datalog evaluation algorithms do indeed have realistic HiLog analogs. The work also compares the performance of these analogs

Discovering Models of Software Processes from Event-Based Data ; CU-CS-819-96

Many software process methods and tools presuppose the existence of a formal model of a process. Unfortunately, developing a formal model for an on-going, complex process can be dicult, costly, and error prone. This presents a practical barrier to the adoption of process technologies, which would be lowered by automated assistance in creating formal models. To this end, we have developed a data analysis technique that we term process discovery. Under this technique, data describing process events are rst captured from an on-going process and then used to generate a formal model of the behavior of that process. In this paper we describe a Markov method that we developed specically for process discovery, as well as describe two additional methods that we adopted from other domains and augmented for our purposes. The three methods range from the purely algorithmic to the purely statistical. We compare the methods and discuss their application in an industrial case study