The Maya Calendar as a Deterministic Finite Automaton: A Formal Computational Analysis of Temporal Synchronization

This publication presents a formal computational analysis of the Maya calendar, specifically the integrated Tzolk’in (260-day), Haab’ (365-day), and Long Count systems. The calendar is rigorously modeled as a deterministic finite automaton with a finite state space of 18,980 unique configurations (Calendar Round), derived from the synchronization of modular cycles. Using tools from discrete mathematics, automata theory, and number theory, the work establishes explicit bounds on state ambiguity, computational complexity for forward and reverse mappings, and intrinsic error-detection properties arising from modular redundancy (GCD(260, 365) = 5). A formal Disaster Recovery Protocol is defined for reconstructing complete Long Count dates from partial or eroded archaeological data. The analysis is strictly mathematical and structural. It does not assert historical intentionality, conscious computational design, or technological awareness on the part of the ancient Maya. Instead, it demonstrates that the calendrical rules admit rigorous formalization and quantifiable performance characteristics when examined through modern formal methods. This work is intended as an open-access research dossier and working paper, suitable for reproducibility, interdisciplinary study, and future extension within computational archaeology, discrete dynamical systems, and the study of ancient calendrical architectures.