Parameterized Formal Graph Systems and Their Polynomial-Time PAC learnability

A formal graph system (FGS for short) is a logic program consisting of definite clauses whose arguments are patterns instead first-order terms. The referred to as rewriting rules. An FGS shown be useful unifying framework learning languages. In this paper, we show the polynomial-time PAC learnability subclass languages defined by parameterized hereditary FGSs with bounded degree, from viewpoint computational theory. That is, consider VH-FGSLk, Δ (m, s, t, r, w, d) class graphs treewidth at most k and maximum degree which variable-hereditary m rules having term arguments. parameters r denote numbers variables, atoms in body, each predicate symbol rule an FGS, respectively. w d number vertices hyperedge vertex has infinitely many even if all constants. Then prove that learnable m, d, constants except k.