Polynomial Time Inductive Inference of TTSP Graph Languages from Positive Data

Abstract

SUMMARYTwo-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 T G T T SP be the set of all TTSP term graphs whose variable labels are mutually distinct. For a TTSP term graph g in T G T T SP , 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 T T SP = {L(g) | g ∈ T G T T SP } is, given a set S of TTSP graphs, to find a TTSP term graph g in T G T T SP 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 T T SP . Finally, we show that L T T SP is polynomial time inductively inferable from positive data. key words: inductive inference,

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