This study explores the cognitive mechanisms underlying human language acquisition through grammar induction by a minimal cognitive architecture, with a short and flexible sequence memory as its most central feature. We use reinforcement learning for the task of identifying sentences in a stream of words from artificial languages. Results demonstrate the model’s ability to identify frequent and informative multi-word chunks, reproducing characteristics of natural language acquisition. The model successfully navigates varying degrees of linguistic complexity, exposing efficient adaptation to combinatorial challenges through the reuse of sequential patterns. The emergence of parsimonious tree structures suggests an optimization for the sentence identification task, balancing economy and information. The cognitive architecture reflects aspects of human memory systems and decision-making processes, enhancing its cognitive plausibility. While the model exhibits limitations in generalization and semantic representation, its minimalist nature offers insights into some fundamental mechanisms of language learning. Our study demonstrates the power of this simple architecture and stresses the importance of sequence memory in language learning. Since other animals do not seem to have faithful sequence memory, this may be a key to understanding why only humans have developed complex languages.