Languages with Decidable Learning: A Meta-theorem

Paul Krogmeier, P. Madhusudan

Research output: Contribution to journalArticlepeer-review


We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined using a bounded amount of auxiliary information that is independent of expression size but depends on a fixed structure over which evaluation occurs. We introduce a generic programming language for writing programs that evaluate expression syntax trees, and we give a meta-theorem that connects such programs for finite-aspect checkable languages to finite tree automata, which allows us to derive new decidable learning results and decision procedures for several expression learning problems by writing programs in the programming language.

Original languageEnglish (US)
Article number80
JournalProceedings of the ACM on Programming Languages
Issue numberOOPSLA1
StatePublished - Apr 6 2023


  • exact learning
  • interpretable learning
  • learning symbolic languages
  • program synthesis
  • tree automata
  • version space algebra

ASJC Scopus subject areas

  • Software
  • Safety, Risk, Reliability and Quality


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