Sep 2026· Zenodo (CERN European Organization for Nuclear Research)
Formal Methods in Verification
Abstract
This note collects the constructions, proofs, and prior-art positioning behind the exact-rational certificates in the Podium library (podium.verify): barrier certificates for abort safety, Karush-Kuhn-Tucker certificates for the online convex solves, control-Lyapunov certificates, sum-of-squares certificates, and an optimality-gap bracket for nonconvex quadratically constrained quadratic programs. None of the underlying certificate mathematics is new; the note documents the exact instantiation, its verification, and its relation to the exact-SOS/moment, rational-SDP-recovery, and QCQP-duality literature, so that a math-inclined reader can audit the certificate layer directly. In detail, guidance and control software relies on numerical optimization and floating-point synthesis whose executions are difficult to verify directly. We study the problem of verifying solver outputs: given a certificate produced by an untrusted floating-point solver, we re-verify it in exact rational arithmetic, so that acceptance constitutes a proof that carries no rounding error. We apply this to four properties: abort safety, via barrier certificates; optimality of the online convex solves, via Karush-Kuhn-Tucker conditions for quadratic and second-order cone programs; closed-loop stability, via Lyapunov ellipsoids from a discrete-time linear-quadratic regulator; and polynomial set containment, via sum-of-squares certificates. For nonconvex quadratically constrained quadratic programs (QCQPs), we specialize the exact rational recovery of a semidefinite certificate (Peyrl-Parrilo; Kaltofen et al.) to the S-procedure dual, yielding a tolerance-free, machine-checkable optimality-gap bracket: a rational lower bound from the S-procedure dual and a rational upper bound from a feasible point, coinciding exactly at a global optimum. The note's original analysis characterizes how the certified lower bound degrades under rational rounding of the dual multiplier: the value loss is second-order in the rounding denominator in the nonsingular case and first-order in the trust-region hard case, with soundness retained in both, and it vanishes when the optimal multiplier is rational. For several constraints the S-procedure need not be tight, and the bracket then certifies a duality gap with both endpoints exact. Each result is accompanied by a verifying test in the reference implementation.
Agile - denoting "the quality of being agile, readiness for motion, nimbleness, activity, dexterity in motion" - software development methods are attempting to offer an answer to the eager business community asking for lighter weight along with faster and nimbler software development processes. This is especially the case with the rapidly growing and volatile Internet software industry as well as for the emerging mobile application environment. The new agile methods have evoked substantial amount of literature and debates. However, academic research on the subject is still scarce, as most of existing publications are written by practitioners or consultants. The aim of this publication is to begin filling this gap by systematically reviewing the existing literature on agile software development methodologies. This publication has three purposes. First, it proposes a definition and a classification of agile software development approaches. Second, it analyses ten software development methods that can be characterized as being "agile" against the defined criterion. Third, it compares these methods and highlights their similarities and differences. Based on this analysis, future research needs are identified and discussed.
P. Abrahamsson, O. Salo, Jussi Ronkainen et al.· arXiv.org· 728 citations· ⚡54
Context: Software startups are newly created companies with no operating history and fast in producing cutting-edge technologies. These companies develop software under highly uncertain conditions, tackling fast-growing markets under severe lack of resources. Therefore, software startups present a unique combination of characteristics which pose several challenges to software development activities. Objective: This study aims to structure and analyze the literature on software development in startup companies, determining thereby the potential for technology transfer and identifying software development work practices reported by practitioners and researchers. Method: We conducted a systematic mapping study, developing a classification schema, ranking the selected primary studies according their rigor and relevance, and analyzing reported software development work practices in startups. Results: A total of 43 primary studies were identified and mapped, synthesizing the available evidence on software development in startups. Only 16 studies are entirely dedicated to software development in startups, of which 10 result in a weak contribution (advice and implications (6); lesson learned (3); tool (1)). Nineteen studies focus on managerial and organizational factors. Moreover, only 9 studies exhibit high scientific rigor and relevance. From the reviewed primary studies, 213 software engineering work practices were extracted, categorized and analyzed. Conclusion: This mapping study provides the first systematic exploration of the state-of-art on software startup research. The existing body of knowledge is limited to a few high quality studies. Furthermore, the results indicate that software engineering work practices are chosen opportunistically, adapted and configured to provide value under the constrains imposed by the startup context.
Nicolò Paternoster, Carmine Giardino, M. Unterkalmsteiner et al.· Information and Software Tec...· 394 citations· ⚡54
The growing literature on affect among software developers mostly reports on the linkage between happiness, software quality, and developer productivity. Understanding happiness and unhappiness in all its components -- positive and negative emotions and moods -- is an attractive and important endeavor. Scholars in industrial and organizational psychology have suggested that understanding happiness and unhappiness could lead to cost-effective ways of enhancing working conditions, job performance, and to limiting the occurrence of psychological disorders. Our comprehension of the consequences of (un)happiness among developers is still too shallow, being mainly expressed in terms of development productivity and software quality. In this paper, we study what happens when developers are happy and unhappy while developing software. Qualitative data analysis of responses given by 317 questionnaire participants identified 42 consequences of unhappiness and 32 of happiness. We found consequences of happiness and unhappiness that are beneficial and detrimental for developers' mental well-being, the software development process, and the produced artifacts. Our classification scheme, available as open data enables new happiness research opportunities of cause-effect type, and it can act as a guideline for practitioners for identifying damaging effects of unhappiness and for fostering happiness on the job.
D. Graziotin, Fabian Fagerholm, Xiaofeng Wang et al.· Journal of Systems and Softw...· 236 citations· ⚡13
Mobile phones have been closed environments until recent years. The change brought by open platform technologies such as the Symbian operating system and Java technologies has opened up a significant business opportunity for anyone to develop application software such as games for mobile terminals. However, developing mobile applications is currently a challenging task due to the specific demands and technical constraints of mobile development. Furthermore, at the moment very little is known about the suitability of the different development processes for mobile application development. Due to these issues, we have developed an agile development approach called Mobile-D. The Mobile-D approach is briefly outlined here and the experiences gained from four case studies are discussed.
P. Abrahamsson, Antti Hanhineva, H. Hulkko et al.· Conference on Object-Oriente...· 225 citations· ⚡18
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