Relational Constraint Driven Test Case Synthesis for Web Applications

This paper proposes a relational constraint driven technique that synthesizes test cases automatically for web applications. Using a static analysis, servlets can be modeled as relational transducers, which manipulate backend databases. We present a synthesis algorithm that generates a sequence of HTTP requests for simulating a user session. The algorithm relies on backward symbolic image computation for reaching a certain database state, given a code coverage objective. With a slight adaptation, the technique can be used for discovering workflow attacks on web applications.Comment: In Proceedings TAV-WEB 2010, arXiv:1009.330

The dominance hierarchy in root systems of Coxeter groups

If $x$ and $y$ are roots in the root system with respect to the standard (Tits) geometric realization of a Coxeter group $W$, we say that $x$ \emph{dominates} $y$ if for all $w\in W$, $wy$ is a negative root whenever $wx$ is a negative root. We call a positive root \emph{elementary} if it does not dominate any positive root other than itself. The set of all elementary roots is denoted by \E. It has been proved by B. Brink and R. B. Howlett (Math. Ann. \textbf{296} (1993), 179--190) that \E is finite if (and only if) $W$ is a finite-rank Coxeter group. Amongst other things, this finiteness property enabled Brink and Howlett to establish the automaticity of all finite-rank Coxeter groups. Later Brink has also given a complete description of the set \E for arbitrary finite-rank Coxeter groups (J. Algebra \textbf{206} (1998)). However the set of non-elementary positive roots has received little attention in the literature. In this paper we answer a collection of questions concerning the dominance behaviour between such non-elementary positive roots. In particular, we show that for any finite-rank Coxeter group and for any non-negative integer $n$, the set of roots each dominating precisely $n$ other positive roots is finite. We give upper and lower bounds for the sizes of all such sets as well as an inductive algorithm for their computation