Polynomial time inductive inference of TTSP graph languages from positive data

  • Authors:

  • Ryoji Takami;Yusuke Suzuki;Tomoyuki Uchida;Takayoshi Shoudai;Yasuaki Nakamura

  • Affiliations:

  • Department of Computer and Media Technologies, Hiroshima City University, Hiroshima, Japan;Faculty of Information Sciences, Hiroshima City University, Hiroshima, Japan;Faculty of Information Sciences, Hiroshima City University, Hiroshima, Japan;Department of Informatics, Kyushu University, Kasuga, Japan;Faculty of Information Sciences, Hiroshima City University, Hiroshima, Japan

  • Venue:
  • ILP'05 Proceedings of the 15th international conference on Inductive Logic Programming
  • Year:
  • 2005

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Abstract

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 $\mathcal{TG_{TTSP}}$ be the set of all TTSP term graphs whose variable labels are mutually distinct. For a TTSP term graph g, 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 $\mathcal{L_{TTSP}}$ = $\{L(g) | g \in \mathcal{TG_{TTSP}}\}$ is, given a set S of TTSP graphs, to find a TTSP term graph g in $\mathcal{TG_{TTSP}}$ 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 $\mathcal{L_{TTSP}}$. Finally, we show that $\mathcal{L_{TTSP}}$ is polynomial time inductively inferable from positive data.