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Explore a 15-minute conference presentation that investigates the synthesis of domain-specific languages (DSLs) for few-shot learning in symbolic domains. Learn about the theoretical foundations of DSL synthesis problems where researchers seek grammars over base languages that ensure small expressions solving training samples also solve corresponding testing samples. Discover the decidability proofs for languages whose semantics over fixed structures can be evaluated by tree automata, particularly when expression size corresponds to parse tree depth in the grammar. Examine how the grammars solving these problems correspond to regular sets of trees and understand the decidability results for problem variants where DSLs only need to express solutions for input learning problems or are defined using macro grammars. Gain insights into the intersection of domain-specific language design, symbolic learning, program synthesis, and tree automata theory through research presented by Paul Krogmeier and P. Madhusudan from the University of Illinois at Urbana-Champaign at the OOPSLA 2025 conference.
