Distributional Learning of Graph Languages Generated by Fixed-Interface Clause Systems

Abstract

Distributional learning provides a useful framework for studying the learnability of structured languages from positive data. In this paper, we extend this framework to graph languages generated by fixed-interface clause systems (FICSs). We formulate FICSs explicitly and study the corresponding learning problem under positive presentations and membership queries. We consider a bounded class of graph languages satisfying the finite context property (FCP) under a bounded-degree assumption. The bounds are expressed by the degree bound $Δ$ together with five structural parameters $m,s,t,w$, and $d$, which control the clause-system structure, interface ranks, and local head-frame complexity. The learning algorithm constructs hypotheses from ordered boundary representations induced by the observed positive examples. These representations make explicit the interface information needed to compare contexts and to test candidate clauses by membership queries. We prove that target contexts eventually appear in the observed sample, target clauses are reconstructed over the corresponding predicate representatives, and spurious non-fact clauses are eventually excluded. Consequently, for every fixed parameter tuple, the target language is identifiable in the limit from positive data and membership queries. We also prove that the learner has polynomial-time update on $\FICSLFCP_Δ(m,s,t,w,d)$: at each stage, only polynomially many ordered boundary representations, predicate symbols, clause candidates, and membership queries are needed. Overall, the paper gives a parameterized reformulation of distributional learning for interface-based graph languages in a fixed-interface setting.