Discovering algorithms with computational language processing.

We present a framework automating algorithm discovery by bootstrapping their natural conceptualization as sequences of operations, represented as tokens. These computational tokens are chained using a grammar, enabling the formation of increasingly sophisticated procedures. Our ensemble Monte Carlo tree search guided by reinforcement learning explores token chaining and drives the creation of new tokens via byte-pair encoding. This methodology rediscovers, improves, and generates new algorithms that substantially outperform existing methods for strongly nondeterministic polynomial-time-hard combinatorial optimization problems and foundational quantum computing approaches such as Grover's and the quantum approximate optimization algorithm. Operating at the computational rather than code-generation level, our framework produces algorithms that can be tailored specifically to problem instances, not merely classes.