Ordered term tree languages which are polynomial time inductively inferable from positive data

Exact Learning of Primitive Formal Systems Defining Labeled Ordered Tree Languages via Queries

“…For each variable h = [v 0 , v 1 ] labeled with x in t, we attach a copy T of T to t by removing h from H(t) and by identifying the vertices v 0 and v 1 with the vertices u 0 and u 1 of T , respectively, where the vertices u 0 and u 1 of T correspond to the vertices u 0 and u 1 of T , respectively. We define a new sibling ordering on every vertex v in t in a natural way [4], [14]. A substitution θ is a finite set of bindings for distinct variable labels.…”

“…A tree language is a set of ordered trees. In order to represent structural features from tree-structured data, we propose an ordered term tree pattern [3], [4], which is a tree pattern that has an ordered tree structure and some internal structured variables. A variable of an ordered term tree pattern has a variable label and can be replaced with an arbitrary ordered tree by hyperedge replacement (see [1]) according to the variable label.…”

“…In this paper, we use an ordered term tree pattern t * as an expression of a target tree language L * such that L * is equal to the tree language defined using t * . We showed in [4] that the class of tree languages defined by ordered term tree patterns is polynomial time inductively inferable from positive data. The query learning model of Angluin [6] is an established mathematical model of learning via queries in computational learning theory.…”

“…For the learning of ordered tree languages, Suzuki et al [4] showed that the class of languages defined by ordered term tree patterns is polynomial time inductively inferable from positive data. Matsumoto et al [9] showed that finite unions of ordered term tree pattern languages are exactly learnable with a polynomial number of queries.…”

“…In Sect. 2, we introduce an ordered term tree pattern [3], [4], a primitive formal ordered tree system and the PSI condition on a pFOTS program, and explain the query learning model [6] briefly. In Sect.…”