Generating Non-Linear Interpolants by Semidefinite Programming

Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed. However, little work focuses on discovering polynomial interpolants in the literature. In this paper, we provide an approach for constructing non-linear interpolants based on semidefinite programming, and show how to apply such results to the verification of programs by examples.Comment: 22 pages, 4 figure

Automatic Abstraction in SMT-Based Unbounded Software Model Checking

Software model checkers based on under-approximations and SMT solvers are very successful at verifying safety (i.e. reachability) properties. They combine two key ideas -- (a) "concreteness": a counterexample in an under-approximation is a counterexample in the original program as well, and (b) "generalization": a proof of safety of an under-approximation, produced by an SMT solver, are generalizable to proofs of safety of the original program. In this paper, we present a combination of "automatic abstraction" with the under-approximation-driven framework. We explore two iterative approaches for obtaining and refining abstractions -- "proof based" and "counterexample based" -- and show how they can be combined into a unified algorithm. To the best of our knowledge, this is the first application of Proof-Based Abstraction, primarily used to verify hardware, to Software Verification. We have implemented a prototype of the framework using Z3, and evaluate it on many benchmarks from the Software Verification Competition. We show experimentally that our combination is quite effective on hard instances.Comment: Extended version of a paper in the proceedings of CAV 201

Non-polynomial Worst-Case Analysis of Recursive Programs

We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs. First, we apply ranking functions to recursion, resulting in measure functions. We show that measure functions provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in nonpolynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$ as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present experimental results to demonstrate that our approach can obtain efficiently worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the divide-and-conquer algorithm for the Closest-Pair problem, where we obtain $\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for polynomial multiplication and Strassen's algorithm for matrix multiplication, where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and close to the best-known bounds for the respective algorithms.Comment: 54 Pages, Full Version to CAV 201

Automatically refining partial specifications for Program Verification

10.1007/978-3-642-21437-0_28Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)6664 LNCS369-38

Lazy Annotation for Program Testing and Verification

Abstract. We describe an interpolant-based approach to test generation and model checking for sequential programs. The method generates Floyd/Hoare style annotations of the program on demand, as a result of failure to achieve goals, in a manner analogous to conflict clause learning in a DPLL style SAT solver.

A Novel Fusion Algorithm to Improve Localisation Accuracy of an Instrumented Bicycle

Cycling is an increasingly popular mode of travel in cities due to the great advantages that it offers in terms of space consumption, health and environmental sustainability, and is therefore favoured and promoted by many city authorities. However, the relatively low perceived safety of cycling from the users’ side currently presents itself as a hurdle towards higher uptake levels of cycling, and unfortunately, road accident statistics (1) confirm this perception as reality. A typical collision pattern observed involves cyclists being “crushed” by turning motorised vehicles, due to their presence in the so-called “blind spot”, which is to the left of the vehicle in the UK and to the right in countries with right - hand traffic (2). Up until a few years ago, th e only options for tackling such a problem would be drawn from the domain of “hard” traffic engineering measures, (usually cost-intensive and/or severely disruptive, such as segregated lanes or vehicle type bans in certain streets). However, trends in the development of ubiquitous computing now offer smaller, more accurate and durable tools to support traffic safety interventions. Examples range from simple passive measures (3) to more advanced experimental active cyclist detection system (4). But while such solutions certainly represent steps in the right direction in terms of preventing cyclist - vehicle collisions, they are limited in what they are unable to perform any reliable prediction of accidents due to their inability to accurately track the cyclist’s trajectory and estimate his/her position in a critical time-horizon of 5-10 seconds. Indeed, the accurate (< 1 m) localisation of the cyclist is a necessity when it comes to preventing collisions, but so far remains an important unresolved challenge, as none of the existing mainstream technologies (GPS, WiFi etc.) can achieve it. Enhanced positioning systems, on the other hand, such as U-blox (5) and Spatial (6) Inertial Navigation System (INS), can achieve accurate positioning in theory, but they are specifically designed for four-wheel vehicles and are therefore very expensive when used for tracking bicycles. Besides, the dynamics of a bicycle is very complex and different from an ordinary vehicle, and so the accuracy of such enhanced positioning syst ems will differ greatly when used on a bicycle. The research reported here focuses on the development and testing of an innovative technological solution for accurately localising and tracking cyclists in urban environments using a low-cost micro-electrome chanical systems (MEMS) sensor configuration on a prototype instrumented bicycle system, called “ iBike ” (7). The ultimate goal is to develop a collision prediction and avoidance system, and the present paper presents a novel fusion technique that could be utilised to improve localisation accuracy based on Wireless Communication Technologies (WCT) widely found in cities as well as Global Navigation Satellite System (GNSS) positioning

Widening Polyhedra with Landmarks: 4th Asian Symposium, APLAS 2006, Sydney, Australia, November 8-10, 2006. Proceedings

The abstract domain of polyhedra is sufficiently expressive to be deployed in verification. One consequence of the richness of this domain is that long, possibly infinite, sequences of polyhedra can arise in the analysis of loops. Widening and narrowing have been proposed to infer a single polyhedron that summarises such a sequence of polyhedra. Motivated by precision losses encountered in verification, we explain how the classic widening/narrowing approach can be refined by an improved extrapolation strategy. The insight is to record inequalities that are thus far found to be unsatisfiable in the analysis of a loop. These so-called landmarks hint at the amount of widening necessary to reach stability. This extrapolation strategy, which refines widening with thresholds, can infer post-fixpoints that are precise enough not to require narrowing. Unlike previous techniques, our approach interacts well with other domains, is fully automatic, conceptually simple and precise on complex loops

Hormones and the auditory system: a review of physiology and pathophysiology

This review explores the potential role of hormones in modulating the auditory function. The review describes four groups of hormones (the hormones of the circathan cycle, reproduction, stress response and the fluid and electrolyte balance), their physiological variations, interactions, as well as the physiological basis for their effect on the auditory system. Possible contribution of hormones to pathophysiology of auditory dysfunctions, including hyperacusis, tinnitus, Meniere's disease and pre-menstrual auditory dysfunction, has also been discussed. Published by Elsevier Ltd on behalf of IBRO