Transformers are Inherently Succinct

We propose succinctness as a measure of the expressive power of a transformer in describing a concept. To this end, we prove that transformers are highly expressive in that they can represent formal languages substantially more succinctly than standard representations of formal languages like finite automata and Linear Temporal Logic (LTL) formulas. As a by-product of this expressivity, we show that verifying properties of transformers is provably intractable (i.e. EXPSPACE-complete).