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We study the Rendezvous problem for 2 autonomous mobile robots inasynchronous settings with persistent memory called light. It is well knownthat Rendezvous is impossible in a basic model when robots have no lights, evenif the system is semi-synchronous. On the other hand, Rendezvous is possible ifrobots have lights of various types with a constant number of colors. If robotscan observe not only their own lights but also other robots' lights, theirlights are called full-light. If robots can only observe the state of otherrobots' lights, the lights are called external-light.  In this paper, we focus on robots with external-lights in asynchronoussettings and a particular class of algorithms (called L-algorithms), where anL-algorithm computes a destination based only on the current colors ofobservable lights. When considering L-algorithms, Rendezvous can be solved byrobots with full-lights and 3 colors in general asynchronous settings (calledASYNC) and the number of colors is optimal under these assumptions. Incontrast, there exists no L-algorithms in ASYNC with external-lights regardlessof the number of colors. In this paper, we consider a fairly large subclass ofASYNC in which Rendezvous can be solved by L-algorithms using external-lightswith a finite number of colors, and we show that the algorithms are optimal inthe number of colors they use.

Optimal Rendezvous ${\mathcal L}$-Algorithms for Asynchronous Mobile Robots with External-Lights