ИСТИНА

Every automaton (a letter-to-letter transducer) whose input/output alphabets consist of p symbols produces a 1-Lipschitz map from p-adic integers to p-adic integers; and vice versa, every that map can be performed by a suitable automaton. Every that map can be regarded as a discrete causal map. By further developing of ideas of our earlier works «Quantization causes waves: Smooth finitely computable functions are affine» (DOI: 10.1134/S2070046615030012) and «Discreteness causes waves» (DOI: 10.2298/FUPCT1603143A) we derive some new results which may serve a base for future automata interpretation of Quantum Theory.