Polynomial Time Inductive Inference of TTSP Graph Languages from Positive Data
Two-Terminal Series Parallel (TTSP, for short) graphs are used as data models in applications for electric networks and scheduling problems. We propose a TTSP term graph which is a TTSP graph having structured variables, that is, a graph pattern over a TTSP graph. Let TG(TTSP) be the set of all TTSP term graphs whose variable labels are mutually distinct. For a TTSP term graph g in TG(TTSP), the TTSP graph language of g, denoted by L(g), is the set of all TTSP graphs obtained from g by substituting arbitrary TTSP graphs for all variables in g. Firstly, when a TTSP graph G and a TTSP term graph g are given as inputs, we present a polynomial time matching algorithm which decides whether or not L(g) contains G. The minimal language problem for the class L(TTSP) = {L(g) vertical bar g is an element of TG(TTSP)} is, given a set S of TTSP graphs, to find a TTSP term graph g in TG(TTSP) such that L(g) is minimal among all TTSP graph languages which contain all TTSP graphs in S. Secondly, we give a polynomial time algorithm for solving the minimal language problem for L(TTSP). Finally, we show that L(TTSP) is polynomial time inductively inferable from positive data.
inductive inference ttsp graph graph languages computational learning theory