Transformers are Inherently Succinct

View PDF HTML (experimental) Abstract: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). Subjects: Formal Languages and Automata Theory (cs.FL); Machine Learning (cs.LG); Logic in Computer Science (cs.LO) Cite as: arXiv:2510.19315 [cs.FL]   (or arXiv:2510.19315v2 [cs.FL] for this version)   https://doi.org/10.48550/arXiv.2510.19315 arXiv-issued DOI via DataCite Submission history From: Pascal Bergsträßer [view email] [v1] Wed, 22 Oct 2025 07:25:54 UTC (28 KB) [v2] Thu, 23 Oct 2025 08:09:19 UTC (28 KB)