Dg Kourie

Efficient automata constructions and approximate automata

In this paper, we present data structures and algorithms for efficiently constructing approximate automata. An approximate automaton for a regular language L is one which accepts at leastL. Such automata can be used in a variety of practical applications, including network security pattern matching, in which false-matches are only a performance nuisance. The construction algorithm is particularly efficient, and is tunable to yield more or less exact automata.

Correctness-by-Construction and Post-hoc Verification: A Marriage of Convenience?

Correctness-by-construction (CbC), traditionally based on weakest precondition semantics, and post-hoc verification (PhV) aspire to ensure functional correctness. We argue for a lightweight approach to CbC where lack of formal rigour increases productivity. In order to mitigate the risk of accidentally introducing errors during program construction, we propose to complement lightweight CbC with PhV. We introduce lightweight CbC by example and discuss strength and weaknesses of CbC and PhV and their combination, both conceptually and using a case study.

Correctness-by-Construction \wedge Taxonomies \Rightarrow Deep Comprehension of Algorithm Families

Correctness-by-construction (CbC) is an approach for developing algorithms inline with rigorous correctness arguments. A high-level specification is evolved into an implementation in a sequence of small, tractable refinement steps guaranteeing the resulting implementation to be correct. CbC facilitates the design of algorithms that are more efficient and more elegant than code that is hacked into correctness. In this paper, we discuss another benefit of CbC, i.e., that it supports the deep comprehension of algorithm families. We organise the different refinements of the algorithms carried out during CbC-based design in a taxonomy. The constructed taxonomy provides a classification of the commonality and variability of the algorithm family and, hence, provides deep insights into their structural relationships. Such taxonomies together with the implementation of the algorithms as toolkits provide an excellent starting point for extractive and proactive software product line engineering.

Light Beam Tracing for Multi-Bounce Specular and Glossy Transport Paths

This paper describes a new extension to light beam tracing that includes glossy multi-bounce transport paths for more realistic rendering of caustics. A spherical Gaussian approximation of the glossy scatter distribution as well as Gauss divergence theorem is used to develop an efficient solution that replaces the irradiance surface integral with a boundary line integral.

Empirically Assessing Algorithm Performance

The timing performance data of ten related algorithms (solving the single keyword pattern matching problem) executing under a wide variety of operating conditions, was gathered and analysed. Using the resulting 15 million items of timing data, various metrics to estimate algorithm performance were computed and compared. An assessment is made of whether and how various changes in the operating environment affect the measurements.