Actions of Maximal Growth

We study acts and modules of maximal growth over finitely generated free monoids and free associative algebras as well as free groups and free group algebras. The maximality of the growth implies some other specific properties of these acts and modules that makes them close to the free ones; at the same time, we show that being a strong "infiniteness" condition, the maximality of the growth can still be combined with various finiteness conditions, which would normally make finitely generated acts finite and finitely generated modules finite-dimensional

Aspects of functional programming

This thesis explores the application of functional programming in new areas and its implementation using new technologies. We show how functional languages can be used to implement solutions to problems in fuzzy logic using a number of languages: Haskell, Ginger and Aladin. A compiler for the weakly-typed, lazy language Ginger is developed using Java byte-code as its target code. This is used as the inspiration for an implementation of Aladin, a simple functional language which has two novel features: its primitives are designed to be written in any language, and evaluation is controlled by declaring the strictness of all functions. Efficient denotational and operational semantics are given for this machine and an implementation is devel- oped using these semantics. We then show that by using the advantages of Aladin (simplicity and strictness control) we can employ partial evaluation to achieve con- siderable speed-ups in the running times of Aladin programs

Around the Domino Problem – Combinatorial Structures and Algebraic Tools

Given a finite set of square tiles, the domino problem is the question of whether is it possible to tile the plane using these tiles. This problem is known to be undecidable in the planar case, and is strongly linked to the question of the periodicity of the tiling. In this thesis we look at this problem in two different ways: first, we look at the particular case of low complexity tilings and second we generalize it to more general structures than the plane, groups. A tiling of the plane is said of low complexity if there are at most mn rectangles of size m × n appearing in it. Nivat conjectured in 1997 that any such tiling must be periodic, with the consequence that the domino problem would be decidable for low complexity tilings. Using algebraic tools introduced by Kari and Szabados, we prove a generalized version of Nivat’s conjecture for a particular class of tilings (a subclass of what is called of algebraic subshifts). We also manage to prove that Nivat’s conjecture holds for uniformly recurrent tilings, with the consequence that the domino problem is indeed decidable for low-complexity tilings. The domino problem can be formulated in the more general context of Cayley graphs of groups. In this thesis, we develop new techniques allowing to relate the Cayley graph of some groups with graphs of substitutions on words. A first technique allows us to show that there exists both strongly periodic and weakly-but-not-strongly aperiodic tilings of the Baumslag-Solitar groups BS(1, n). A second technique is used to show that the domino problem is undecidable for surface groups. Which provides yet another class of groups verifying the conjecture saying that the domino problem of a group is decidable if and only if the group is virtually free

Core Technologies for Native XML Database Management Systems

This work investigates the core technologies required to build Database Management Systems (DBMSs) for large collections of XML documents. We call such systems XML Base Management Systems (XBMSs). We identify requirements, and analyze how they can be met using a conventional DBMS. Our conclusion is that an XML support layer on top of an existing conventional DBMS does not address the requirements for XBMSs. Hence, we built a Native XBMS, called Natix. Natix has been developed completely from scratch, incorporating optimizations for high-performance XML processing in those places where they are most effective

ITL Monitor: Compositional Runtime Analysis with Interval Temporal Logic

Runtime verification has gained significant interest in recent years. It is a process in which the execution trace of a program is analysed while it is running. A popular language for specifying temporal requirements for runtime verification is Linear Temporal Logic (LTL), which is excellent for expressing properties such as safety and liveness. Another formalism that is used is Interval Temporal Logic (ITL). This logic has constructs for specifying the behaviour of programs that can be decomposed into subintervals of activity. Traditionally, only a restricted subset of ITL has been used for runtime verification due to the limitations imposed by making the subset executable. In this thesis an alternative restriction of ITL was considered as the basis for constructing a library of runtime verification monitors (ITL-Monitor). The thesis introduces a new first-occurrence operator (|>) into ITL and explores its properties. This operator is the basis of the translation from runtime monitors to their corresponding ITL formulae. ITL-Monitor is then introduced formally, and the algebraic properties of its operators are analysed. An implementation of ITL-Monitor is given, based upon the construction of a Domain Specific Language using Scala. The architecture of the underlying system comprises a network of concurrent actors built on top of Akka - an industrial strength distributed actor framework. A number of example systems are constructed to evaluate ITL-Monitor's performance against alternative verification tools. ITL-Monitor is also subjected to a simulation that generates a very large quantity of state data. The monitors were observed to deliver consistent performance across execution traces of up to a million states, and to verify subintervals of up to 300 states against ITL formulae with evaluation complexity of O(n^3)

1977 March, Memphis State University bulletin

Vol. 66, No. 2 of the Memphis State University bulletin containing the graduate catalog for 1977-78, 1977 March.https://digitalcommons.memphis.edu/speccoll-ua-pub-bulletins/1144/thumbnail.jp

1972 February, Memphis State University bulletin

Vol. 61, No. 1 of the Memphis State University bulletin containing the undergraduate catalog for 1972-73, 1972 February.https://digitalcommons.memphis.edu/speccoll-ua-pub-bulletins/1122/thumbnail.jp

1974 February, Memphis State University bulletin

Vol. 63, No. 1 of the Memphis State University bulletin containing the undergraduate catalog for 1974-75, 1974 February.https://digitalcommons.memphis.edu/speccoll-ua-pub-bulletins/1126/thumbnail.jp

1973 February, Memphis State University bulletin

Vol. 62, No. 1 of the Memphis State University bulletin containing the undergraduate catalog for 1973-74, 1973 February.https://digitalcommons.memphis.edu/speccoll-ua-pub-bulletins/1124/thumbnail.jp