8,112 research outputs found
Review of Richard Healey, Gauging What's Real.
Review of Richard Healey's 2008 book. To appear in MIND
An exercise in transformational programming: Backtracking and Branch-and-Bound
We present a formal derivation of program schemes that are usually called Backtracking programs and Branch-and-Bound programs. The derivation consists of a series of transformation steps, specifically algebraic manipulations, on the initial specification until the desired programs are obtained. The well-known notions of linear recursion and tail recursion are extended, for structures, to elementwise linear recursion and elementwise tail recursion; and a transformation between them is derived too
Facilitating modular property-preserving extensions of programming languages
We will explore an approach to modular programming language descriptions and extensions in a denotational style.
Based on a language core, language features are added stepwise on the core. Language features can be described
separated from each other in a self-contained, orthogonal way. We present an extension semantics framework consisting
of mechanisms to adapt semantics of a basic language to new structural requirements in an extended language
preserving the behaviour of programs of the basic language. Common templates of extension are provided. These
can be collected in extension libraries accessible to and extendible by language designers. Mechanisms to extend
these libraries are provided. A notation for describing language features embedding these semantics extensions is
presented
On Region Algebras, XML Databases, and Information Retrieval
This paper describes some new ideas on developing a logical algebra for databases that manage textual data and support information retrieval functionality. We describe a first prototype of such a system
Deriving real-time action systems with multiple time bands using algebraic reasoning
The verify-while-develop paradigm allows one to incrementally develop programs from their specifications using a series of calculations against the remaining proof obligations. This paper presents a derivation method for real-time systems with realistic constraints on their behaviour. We develop a high-level interval-based logic that provides flexibility in an implementation, yet allows algebraic reasoning over multiple granularities and sampling multiple sensors with delay. The semantics of an action system is given in terms of interval predicates and algebraic operators to unify the logics for an action system and its properties, which in turn simplifies the calculations and derivations
Issues about the Adoption of Formal Methods for Dependable Composition of Web Services
Web Services provide interoperable mechanisms for describing, locating and
invoking services over the Internet; composition further enables to build
complex services out of simpler ones for complex B2B applications. While
current studies on these topics are mostly focused - from the technical
viewpoint - on standards and protocols, this paper investigates the adoption of
formal methods, especially for composition. We logically classify and analyze
three different (but interconnected) kinds of important issues towards this
goal, namely foundations, verification and extensions. The aim of this work is
to individuate the proper questions on the adoption of formal methods for
dependable composition of Web Services, not necessarily to find the optimal
answers. Nevertheless, we still try to propose some tentative answers based on
our proposal for a composition calculus, which we hope can animate a proper
discussion
Cylindrical Algebraic Sub-Decompositions
Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic
geometry, used primarily for eliminating quantifiers over the reals and
studying semi-algebraic sets. In this paper we introduce cylindrical algebraic
sub-decompositions (sub-CADs), which are subsets of CADs containing all the
information needed to specify a solution for a given problem.
We define two new types of sub-CAD: variety sub-CADs which are those cells in
a CAD lying on a designated variety; and layered sub-CADs which have only those
cells of dimension higher than a specified value. We present algorithms to
produce these and describe how the two approaches may be combined with each
other and the recent theory of truth-table invariant CAD.
We give a complexity analysis showing that these techniques can offer
substantial theoretical savings, which is supported by experimentation using an
implementation in Maple.Comment: 26 page
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