A134342 Accepted inputs by a certain adaptive automaton (number 4258072) with two adaptive functions and unary numbers as input.

0, 2, 5, 9, 15, 24, 38, 59, 90, 137, 207, 312, 470, 707, 1062, 1595, 2394, 3593, 5391, 8088

Offset: 0

Author

Nicolau Leal Werneck (nwerneck(AT)gmail.com), Jan 16 2008

Keywords

• hard
• nonn
• uned

Comments

This sequence comes from an adaptive finite automaton. These are the numbers (entered in unary base) accepted by the machine. This automaton grows as a ring, with transitions that collect the input symbols and there are two adaptive functions: F and G. F creates a new state between the next state and the state after it, with the G function being called in the transition after the new one. The G function makes the transition a clean one and makes the following transition call the F function. These functions are activated before the transition take place (they are "pre" functions). The initial machine has a single state, which is the final state and a transition to itself with the F function. The automaton grows as a ring and the function calls to F and G move around the machine, making the ring grown in an (apparently) erratic and chaotic fashion.

A program is needed to simulate adaptive finite automata. The machine can be described by the following program in the SDMBA language: FUN PRE F: GEN; * 1 T11 G; T1 1 *; END; FUN PRE G: T1 1 T11 F; END; q1 1 q1 F; INIT q1; FINAL q1; (T, T1 and T11 mean the current state ("this"), the next state and the one after it. * means the newly created state. The body of the functions describe the adaptive actions, which are transition specifications. The "1" means the consumed symbol and the "F" or "G" at the end are the functions to be called (which can be none).)

References

• J. J. Neto, Adaptive Rule-Driven Devices - General Formulation and Case Study, CIAA(2001)
• J. J. Neto, Adaptive automata for context-dependent languages, SIGPLAN Notices, 29(9) (1994) pp. 115-124
• Future article about research on adaptive finite automata with simple rules and complex behavior.

Links

• Nicolau Werneck, Adaptoide, a library for adaptive finite automata. Source code in C++ available.
• João José Neto, Adaptive Rule-Driven Devices - General Formulation and Case Study, CIAA (2001)
• João José Neto, Adaptive automata for context-dependent languages, SIGPLAN Notices, 29(9) (1994) pp. 115-124.
• Yaohui Zhu, Kaiming Sun, Zhengdong Luo, and Lingfeng Wang, Progressive Self-Learning for Domain Adaptation on Symbolic Regression of Integer Sequences, Proc. 39th AAAI Conf. Artif. Intel. (2025) Vol. 39, No. 1, 1692-1699. See p. 1698.

Formula

FUN PRE F: GEN; * 1 T11 G; T1 1 *; END; FUN PRE G: GEN; T1 1 T11 F; T 1 T1; END; q1 1 q1 F; INIT q1; FINAL q1;