Оlympiad Tasks in Changing Environment

Traditionally, tasks in informatics are formulated within fixed (discrete) environment such as segments (1..N), rectangles (1..N × 1..M), or graphs containing various objects, obstacles, connections, and goals. However, in practice environment often change dynamically, and the information available is incomplete, which makes standard algorithmic solutions inadequate. Likewise, a living agent perceives only nearby elements of its environment. This paper explores a class of tasks that address these limitations. Some of these tasks were generated with the assistance of AI. The concepts of timexels (introduced by the authors in their prior work) and program time are used as foundational tools to describe changing discrete environments. Keywords: Olympiad, informatics, task design, dynamic environment, motion, timexel, program time.