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We propose an approach to quantify interference in a simple imperative language that includes a looping construct. In this paper we focus on a particular case of this definition of interference: leakage of information from private variables to public ones via a Trojan Horse attack. We quantify leakage in terms of Shannon's information theory and we motivate our definition by proving a result relating this definition of leakage and the classical notion of programming language interference. The major contribution of the paper is a quantitative static analysis based on this definition for such a language. The analysis uses some non-trivial information theory results like Fano's inequality and L1 inequalities to provide reasonable bounds for conditional statements. While-loops are handled by integrating a qualitative flow-sensitive dependency analysis into the quantitative analysis.

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Abstract-A common and natural intuition among software testers is that test cases need to differ if a software system is to be tested properly and its quality ensured. Consequently, much research has gone into formulating distance measures for how test cases, their inputs and/or their outputs differ. However, common to these proposals is that they are data type specific and/or calculate the diversity only between pairs of test inputs, traces or outputs.We propose a new metric to measure the diversity of sets of tests: the test set diameter (TSDm). It extends our earlier, pairwise test diversity metrics based on recent advances in information theory regarding the calculation of the normalized compression distance (NCD) for multisets. An advantage is that TSDm can be applied regardless of data type and on any test-related information, not only the test inputs. A downside is the increased computational time compared to competing approaches.Our experiments on four different systems show that the test set diameter can help select test sets with higher structural and fault coverage than random selection even when only applied to test inputs. This can enable early test design and selection, prior to even having a software system to test, and complement other types of test automation and analysis. We argue that this quantification of test set diversity creates a number of opportunities to better understand software quality and provides practical ways to increase it.

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Failed error propagation (FEP) is known to hamper software testing, yet it remains poorly understood. We introduce an information theoretic formulation of FEP that is based on measures of conditional entropy. This formulation considers the situation in which we are interested in the potential for an incorrect program state at statement s to fail to propagate to incorrect output. We define five metrics that differ in two ways: whether we only consider parts of the program that can be reached after executing s and whether we restrict attention to a single program path of interest. We give the results of experiments in which it was found that on average one in 10 tests suffered from FEP, earlier studies having shown that this figure can vary significantly between programs. The experiments also showed that our metrics are well-correlated with FEP. Our empirical study involved 30 programs, for which we executed a total of 7,140,000 test cases. The results reveal that the metrics differ in their performance but the Spearman rank correlation with failed error propagation is close to 0.95 for two of the metrics. These strong correlations in an experimental setting, in which all information about both FEP and conditional entropy is known, open up the possibility in the longer term of devising inexpensive information theory based metrics that allow us to minimise the effect of FEP.

A topological quasi-variety Q + T (M ∼ ) := IScP + M ∼ generated by a finite algebra M ∼with the discrete topology is said to be standard if it admits a canonical axiomatic description. Drawing on the formal language notion of syntactic congruences, we prove that Q + T (M ∼ ) is standard provided that the algebraic quasi-variety generated by M ∼ is a variety, and that syntactic congruences in that variety are determined by a finite set of terms. We give equivalent semantic and syntactic conditions for a variety to have Finitely Determined Syntactic Congruences (FDSC), show that FDSC is equivalent to a natural generalisation of Definable Principle Congruences (DPC) which we call Term Finite Principle Congruences (TFPC), and exhibit many familiar algebras M ∼ that our method reveals to be standard. As an application of our results we show, for example, that every Boolean topological lattice belonging to a finitely generated variety of lattices is profinite and that every Boolean topological group, semigroup, and ring is profinite. While the latter results are well known, the result on lattices was previously known only in the distributive case. Background, motivation and overview of resultsAn algebra M = M ; F with finite underlying set M and operations F generates an (algebraic) quasi-variety Q(M) := ISP M consisting of all isomorphic copies of subalgebras of direct powers of M. Similarly a structure M ∼ = M ; G, H, R, T with finite underlying set M , operations G, partial operations H, relations R and discrete topology T generates a topological quasi-variety Q + T (M ∼ ) := IS c P + M ∼ consisting of all isomorphic copies of topologically closed substructures of non-zero direct powers, with the product topology, of M ∼ . Interest in topological quasi-varieties stems from the fact that they arise as the duals to algebraic quasi-varieties under natural dualities. The general theory of natural dualities provides methods to Presented by R. W. Quackenbush.

We investigate first-order axiomatic descriptions of naturally occurring classes of Boolean topological structures (these structures can have operations and relations, and carry a compatible compact Hausdorff topology with a basis of clopen sets). Our methods utilize inverse limits and ultraproducts of finite structures. We illustrate the range of possible axiomatizations of these classes with applications of our methods to Boolean topological lattices, graphs, ordered structures, unary algebras and semigroups. For example, whereas the class of all k-colorable graphs is known to be axiomatizable by universal Horn sentences, we find the class of continuously k-colorable Boolean topological graphs is not even first-order axiomatizable.