Grammar systems theory

Grammar systems theory is the field of theoretical computer science which study systems of finite collection of formal grammars generating a formal language. Each grammar works on a string so-called sequential form that represents an environment. Grammar system can thus be used as an formalization of decentralized or distributed systems of agents in AI.

Agent representation

Let $\mathbb {A}$ to be a simple reactive agent moving on the table and trying not to fall down from the table with two reactions $t$ for turning and $f$ for moving forward. The set of possible behaviors of $\mathbb {A}$ can then be described as an formal language $\mathbb {L_{A}} =\{(f^{m}t^{n}f^{r})^{+}:1\leq m\leq k;1\leq n\leq l;1\leq r\leq k\}$, where $k$ and $l$ are dimensions of the table.

Let $\mathbb {G_{A}}$ to be a formal grammar which generates language $\mathbb {L_{A}}$. The behavior of $\mathbb {A}$ is then described by this grammar.