An orbital construction of optimum distance flag codes

Flag codes are multishot network codes consisting of sequences of nested subspaces (flags) of a vector space Fnq, where q is a prime power and Fq, the finite field of size q. In this paper we study the construction on F2kq of full flag codes having maximum distance (optimum distance full flag codes) that can be endowed with an orbital structure provided by the action of a subgroup of the general linear group. More precisely, starting from a subspace code of dimension k and maximum distance with a given orbital description, we provide sufficient conditions to get an optimum distance full flag code on F2kq having an orbital structure directly induced by the previous one. In particular, we exhibit a specific orbital construction with the best possible size from an orbital construction of a planar spread on F2kq that strongly depends on the characteristic of the field.The authors receive financial support from Ministerio de Ciencia e Innovación (PID2019-108668GB-I00). The second author is supported by Generalitat Valenciana and Fondo Social Europeo (ACIF/2018/196)

A TYPE ANALYSIS OF REWRITE STRATEGIES

Rewrite strategies provide an algorithmic rewriting of terms using strategic compositions of rewrite rules. Due to the programmability of rewrites, errors are often made due to incorrect compositions of rewrites or incorrect application of rewrites to a term within a strategic rewriting program. In practical applications of strategic rewriting, testing and debugging becomes substantially time-intensive for large programs applied to large inputs derived from large term grammars. In essence, determining which rewrite in what position in a term did or did not re comes down to logging, tracing and/or di -like comparison of inputs to outputs. In this thesis, we explore type-enabled analysis of strategic rewriting programs to detect errors statically. In particular, we introduce high-precision types to closely approximate the dynamic behavior of rewriting. We also use union types to track sets of types due to presence of strategic compositions. In this framework of high-precision strategic typing, we develop and implement an expressive type system for a representative strategic rewriting language TL. The results of this research are sufficiently broad to be adapted to other strategic rewriting languages. In particular, the type-inferencing algorithm does not require explicit type annotations for minimal impact on an existing language. Based on our experience with the implementation, the type system significantly reduces the time and effort to program correct rewrite strategies while performing the analysis on the order of thousands of source lines of code per second

Axiomatic and tableau-based reasoning for Kt(H,R)

We introduce a tense logic, called Kt(H, R), arising from logics for spatial reasoning. Kt(H, R) is a multi-modal logic with two modalities and their converses defined with respect to a pre-order and a relation stable over this pre-order. We show Kt(H,R) is decidable, it has the effective finite model property and reasoning in Kt(H,R) is PSPACE-complete. Two complete Hilbert-style axiomatisations are given. The main focus of the paper is tableau-based reasoning. Our aim is to gain insight into the numerous possibilities of defining tableau calculi and their properties. We present several labelled tableau calculi for Kt(H,R) in which the theory rules range from accommodating correspondence properties closely, to accommodating Hilbert axioms closely. The calculi provide the basis for decision procedures that have been imple- mented and tested on modal and intuitionistic problems

FORM: The FORTRAN Object Recovery Model. A Methodology to Extract Object-Oriented Designs From Imperative Code.

A majority of legacy systems in use in the scientific and engineering application domains are coded in imperative languages, specifically, COBOL or FORTRAN-77. These systems have an average age of 15 years or more and have undergone years of extensive maintenance. They suffer from either poor documentation or no documentation, and antiquated coding practices and paradigms (Chik94) (Osbo90). The purpose of this research is to develop a reverse-engineering methodology to extract an object-oriented design from legacy systems written in imperative languages. This research defines a three-phase methodology that inputs source code and outputs an object-oriented design. The three phases of the methodology include: Object Extraction, Class Abstraction, and Formation of the Inheritance Hierarchy. Additionally, there is a pre-processing phase that involves code structuring, alias resolution, and resolution of the COMMON block. Object Extraction is divided into two stages: Attribute Identification and Method Identification. The output of phase one is a set of candidate objects that will serve as input for phase two, Class Abstraction. The Class Abstraction phase uses clustering techniques to form classes and define the concept of identical objects. The output of phase two is a set of classes that will serve as input to the third phase, Formation of the Inheritance Hierarchy. The Formation of the Inheritance Hierarchy phase defines a similarity measure which determines class similarity and further refines the clustering performed in phase two, Class Abstraction. The result of the methodology is an object-oriented design including hierarchy diagrams and interaction diagrams. Additionally, the results of applying the methodology in two case studies are presented. The research has resulted in the development of a unique methodology to extract object-oriented designs from imperative legacy systems. The benefits of using the methodology include: the ability to capture system functionality which may not be apparent due to poor system structure, and the reduction of future maintenance costs of the system as a direct effect of accurate system documentation and updated programming technologies

A Concurrent Reactive Esterel Processor based on Multi-Threading

The synchronous language Esterel is well-suited for programming control-dominated reactive systems at the system level. It provides non-traditional control structures, in particular concurrency and various forms of preemption, which allow to concisely express reactive behavior. As these control structures cannot be mapped easily onto traditional, sequential processors, an alternative approach that has emerged recently makes use of special-purpose reactive processors. However, the designs proposed so far have limitations regarding completeness of the language support, and did not really take advantage of compile-time knowledge to optimize resource usage. This paper presents a reactive processor, the Kiel Esterel Processor 3a (KEP3a), and its compiler. The KEP3a improves on earlier designs in several areas; most notable are the support for exception handling and the provision of context-dependent preemption handling instructions. The KEP3a compiler presented here is to our knowledge the first for multi-threaded reactive processors. The translation of Esterel's preemption constructs onto KEP3a assembler is straightforward; however, a challenge is the correct and efficient representation of Esterel's concurrency. The compiler generates code that respects data and control dependencies using the KEP3a priority-based scheduling mechanism. We present a priority assignment approach that makes use of a novel concurrent control flow graph and has a complexity that in practice tends to be linear in the size of the program. Unlike earlier Esterel compilation schemes, this approach avoids unnecessary context switches by considering each thread's actual execution state at run time. Furthermore, it avoids code replication present in other approaches