A Brief History of Singlefold Diophantine Definitions

Consider an (m + 1)-ary relation R over the set N of natural numbers. Does there exist an arithmetical formula ZΘ(a0, . . . , am, x1, . . . , xK), not involving universal quantifiers, negation, or implication, such that the representation and univocity conditions, viz., (Formula Presented) are met by each tuple (Formula Presented). A priori, the answer may depend on the richness of the language of arithmetic: Even if solely addition and multiplication operators (along with the equality relator and with positive integer constants) are adopted as primitive symbols of the arithmetical signature, the graph R of any primitive recursive function is representable; but can representability be reconciled with univocity without calling into play one extra operator designating either the dyadic operation [b, n]↠ b n or just the monadic function n ↠ b n associated with a fixed integer b > 1? As a preparatory step toward a hoped-for positive answer to this question, one may consider replacing the exponentiation operator by a dyadic relator designating an exponential-growth relation (a notion made explicit by Julia Bowman Robinson in 1952). We will discuss the said univocity, aka ‘single-fold-ness’, issue-first raised by Yuri V. Matiyasevich in 1974-, framing it in historical context. © 2023 Copyright for this paper by its authors

model driven reverse engineering approaches a systematic literature review

This paper explores and describes the state of the art for what concerns the model-driven approaches proposed in the literature to support reverse engineering. We conducted a systematic literature review on this topic with the aim to answer three research questions. We focus on various solutions developed for model-driven reverse engineering, outlining in particular the models they use and the transformations applied to the models. We also consider the tools used for model definition, extraction, and transformation and the level of automation reached by the available tools. The model-driven reverse engineering approaches are also analyzed based on various features such as genericity, extensibility, automation of the reverse engineering process, and coverage of the full or partial source artifacts. We describe in detail and compare fifteen approaches applying model-driven reverse engineering. Based on this analysis, we identify and indicate some hints on choosing a model-driven reverse engineering approach from the available ones, and we outline open issues concerning the model-driven reverse engineering approaches