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Top1. Introduction
The rapid growth of computing devices has led to the emergence of distributed user interfaces (DUI). A DUI provides for interaction between a user and an interface using several devices simultaneously, which increases application usability (Elmqvist, 2011). Presently, the following DUI implementations exist:
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Synchronization system between a smartphone and a smartwatch, where the latter can perform some of the smartphone functions (Nascimento, Oliveira, & Tam, 2018);
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Device management using a smartphone or a tablet (Stojkoska & Trivodaliev, 2017);
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DUI for generating a shopping list at a supermarket (Ghiani, Manca, & Paternò, 2015);
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DUI for collaborative decision making (Widjaja & Takahashi, 2016).
The said DUI implementations are developed using supplementary software tools (Nebeling & Dey, 2016; Yang & Wigdor, 2014; Chi, Li, & Hartmann, 2016). The tools in turn rely on distribution templates (Tesoriero & Altalhi, 2017) presented in special formats. In particular, the MARIA format (Manca & Paternò, 2011) is designed to describe a distributed abstract interface and its implementation across various devices. The indicated tools and templates do not contain distribution rules. They are used for developing software for particular applications and devices. In the article (Penalver, López-Espín, Gallud, Lazcorreta, & Botella, 2011) devoted to device synchronization in the DUI, the authors introduce the following formal synchronization properties: correctness, consistency, decomposability, portability, simultaneity, and continuity. But distribution rules were not strictly defined.
Every time you design a new DUI, a new dynamic logic for the distribution of interface elements has to be developed as well. This logic may be far from trivial and heavily dependent on developer's preferences. At this point, it is difficult to introduce the DUI concept to general public as an average user struggles to comprehend the distribution logic behind it and is reluctant to learn new interaction methods (Sakulin, Alfimtsev, Solovyev, & Sokolov, 2018). On the other hand, it implies significant labor effort from developers, considering that the complexity of DUI elements distribution increases exponentially (Gallud, Tesoriero, Vanderdonckt, Lozano, Penichet, & Botella, 2011). For example, to distribute a two-element interface to two devices, you need to consider nine possible scenarios since one element of the DUI can be distributed to either of the two devices or to both.
For the foregoing reasons, developing formal methods for distributing interface elements appears to be an anticipated next step. Section 2.1 contains a formal description of the developed distribution rules. Section 2.3 describes the example adaptation of the pi-calculus to the distribution description. Section 3 contains the results of the usability testing of a distributed interface designed according to the distribution rules from Section 2.1.