Further reading

Gold supplies the classical language-identification template [ Gold , 1965 , 1967 ] . Angluin gives the canonical active-learning result for regular languages from membership and equivalence queries [ Angluin , 1987 ] ; Rivest and Schapire replace global-state enumeration by a diversity representation built from equivalence classes of tests [ Rivest and Schapire , 1994 ] . Krohn and Rhodes give the prime decomposition of finite machines [ Krohn and Rhodes , 1965 ] ; Ronca et al. [ 2023 ] develop its modern sample-complexity consequences for learnable cascades; and categorical extensions are given by Wells [ 1980 , 1988 ] , Thérien [ 1991 ] . The stochastic direction begins with the support-semigroup decomposition of Carlsson and Yu [ 2015 ] ; Plotkin and Plotkin [ 2015 ] provide a related decomposition theory for linear automata using triangular and wreath products. Liu et al. [ 2023 ] connect Krohn–Rhodes factors to shallow Transformer simulation and document both learnable shortcuts and their generalization failures. Rutten develops the coalgebraic account of automata, behavior, bisimulation, and coinduction [ Rutten , 2000 ] . Predictive state representations isolate prediction from hidden-state ontology and control [ Littman et al. , 2001 ] . Puterman and Sutton–Barto develop the MDP and reinforcement-learning frameworks [ Puterman , 1994 , Sutton and Barto , 2018 ] ; the options framework promotes closed-loop behaviors into temporally extended actions with explicit initiation and termination interfaces [ Sutton et al. , 1999 ] . Pearl and Peters, Janzing, and Schölkopf develop causal models and causal discovery [ Pearl , 2009 , Peters et al. , 2017 ] . Transformer sequence modeling is introduced by Vaswani et al. [ 2017 ] ; world models and joint-embedding predictive approaches are represented by Ha and Schmidhuber [ 2018 ] , LeCun [ 2022 ] , Assran et al. [ 2023 ] . RoboDreamer provides an embodied example in which language components and multimodal goals compose conditional video models for unseen robot tasks [ Zhou et al. , 2024 ] ; PoE-World composes LLM-synthesized programmatic experts into a stochastic world model and tests few-observation planning and generalization in Atari environments [ Piriyakulkij et al. , 2025 ] ; and COMBO combines partial-view state estimation, agent-wise diffusion factors, VLM-based intent and action modules, and tree search for embodied cooperation [ Zhang et al. , 2025 ] . The next two chapters turn this comparison into the explicit UOCL machine and its persistence theory.