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We compare two methods for software specification: <em>algebraic specifications</em> and automata. While algebraic specifications have been around since the 1970s and have been studied extensively, specification by automata is relatively new. Its origins are in another veteran method called <em>trace assertions</em>, which considers a software module as a set of traces, that is, a sequences of function executions. A module is specified by a set of canonical traces and an equivalence relation matching one of the canonical traces to each non-canonical trace. It has been recently shown that trace assertions is an equivalent method to specification by automata. In continuation of this work on trace assertions and automata, we study how automata compare with algebraic specifications. We prove that every specification using an automaton can be converted into an algebraic specification describing the same abstract data type. This conversion utilises a set of canonical words, representing states in the automaton. We next consider varieties of monoids as a heuristic for obtaining more concise algebraic specifications from automata. Finally, we discuss the opposite conversion of algebraic specifications into automata. We show that, while an automaton always exists for every abstract data type described by an algebraic specification, this automaton may not be finitely describable and therefore may not be considered as a viable method for software specification.

Call number: LD2668 .T4 1959 S56

Call number: LD2668 .T4 1958 G65 / Master of Science

Thesis advisor: Ben Howard / The results in this dissertation are on the intersection behavior of certain special cycles on GSpin(n, 2) Shimura varieties for n > 1. In particular, we will determine when the intersection of the special cycles defined by a collection of special endomorphisms consists of isolated points in terms of the fundamental matrix of this collection. These generalize the corresponding results in the lower dimensional cases proved by Kudla and Rapoport. / Thesis (PhD) — Boston College, 2017. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

by Leung Wai-Man Raymond. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves [1]-[3] (2nd gp.)). / Chapter CHAPTER 0 --- Introduction --- p.1 / Chapter CHAPTER 1 --- Einstein-Hermitian Vector Bundles / Chapter 1.1 --- Preliminaries on Einstein-Hermitian structures --- p.4 / Chapter 1.2 --- Conformal invariance --- p.7 / Chapter 1.3 --- A Chern number inequality --- p.9 / Chapter CHAPTER 2 --- Stable Vector Bundles / Chapter 2.1 --- Coherent analytic sheaves --- p.12 / Chapter 2.2 --- "Torsion-free, reflexive and normal coherent analytic sheaves" --- p.18 / Chapter 2.3 --- Determinant bundles --- p.22 / Chapter 2.4 --- Stable vector bundles --- p.27 / Chapter 2.5 --- Stability of Einstein-Hermitian vector bundles --- p.32 / Chapter CHAPTER 3 --- Existence of Einstein-Hermitian connection on stable vector bundle over a compact Riemann Surface --- p.34 / Chapter CHAPTER 4 --- Existence of Einstein-Hermitian metric on stable vector bundle over a projective algebraic manifold / Chapter 4.1 --- Solution of the evolution equation for finite time --- p.45 / Chapter 4.2 --- Convergence of solution for infinite time --- p.53 / APPENDIX / Chapter I. --- A vanishing theorem of Bochner type and its consequences --- p.67 / Chapter II. --- Uhlenbeck's results on connections with Lp bounds on curvature --- p.69 / REFERENCE

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