A BDD-Based Algorithm for Learning from Interpretation Transition

In recent years, there has been an extensive interest in learning the dynamics of systems. For this purpose, a new learning method called learning from interpretation transition has been proposed recently [1]. However, both the run time and the memory space of this algorithm are exponential, so a better data structure and an efficient algorithm have been awaited. In this paper, we propose a new learning algorithm of this method utilizing an efficient data structure inspired from Ordered Binary Decision Diagrams. We show empirically that using this representation we can perform the same learning task faster with less memory space.

[1]  S. Kauffman Metabolic stability and epigenesis in randomly constructed genetic nets. , 1969, Journal of theoretical biology.

[2]  Maxim Teslenko,et al.  A SAT-Based Algorithm for Finding Attractors in Synchronous Boolean Networks , 2011, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[3]  Katsumi Inoue,et al.  Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence Logic Programming for Boolean Networks , 2022 .

[4]  Thomas G. Dietterich What is machine learning? , 2020, Archives of Disease in Childhood.

[5]  F. R. A. Hopgood,et al.  Machine Intelligence 5 , 1971, The Mathematical Gazette.

[6]  Jack Minker Foundations of deductive databases and logic programming , 1988 .

[7]  Shin-ichi Minato,et al.  Zero-Suppressed BDDs for Set Manipulation in Combinatorial Problems , 1993, 30th ACM/IEEE Design Automation Conference.

[8]  Karem A. Sakallah,et al.  ZBDD-Based Backtrack Search SAT Solver , 2002, IWLS.

[9]  Chen-Shang Lin,et al.  On the OBDD-Representation of General Boolean Functions , 1992, IEEE Trans. Computers.

[10]  Tsutomu Sasao,et al.  Logic Synthesis and Verification , 2013 .

[11]  Jan Friso Groote,et al.  Binary decision diagrams for first-order predicate logic , 2003, J. Log. Algebraic Methods Program..

[12]  GusfieldDan Introduction to the IEEE/ACM Transactions on Computational Biology and Bioinformatics , 2004 .

[13]  Christoph Meinel,et al.  Ordered binary decision diagrams , 2001 .

[14]  Luc De Raedt,et al.  ProbLog: A Probabilistic Prolog and its Application in Link Discovery , 2007, IJCAI.

[15]  Hiroki Arimura,et al.  Frequent closed item set mining based on zero-suppressed BDDs (論文特集:データマイニングと統計数理) , 2007 .

[16]  Sheldon B. Akers,et al.  Binary Decision Diagrams , 1978, IEEE Transactions on Computers.

[17]  Katsumi Inoue,et al.  In defense of PDDL axioms , 2003, Artif. Intell..

[18]  Chiaki Sakama,et al.  Learning from interpretation transition , 2013, Machine Learning.

[19]  E. Hill Journal of Theoretical Biology , 1961, Nature.

[20]  Luc De Raedt,et al.  ILP turns 20 , 2011, Machine Learning.

[21]  Gordon Plotkin,et al.  A Further Note on Inductive Generalization , 2008 .

[22]  Gordon Plotkin,et al.  A Note on Inductive Generalization , 2008 .

[23]  Robert A. Kowalski,et al.  The Semantics of Predicate Logic as a Programming Language , 1976, JACM.

[24]  Sofia Cassel,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 2012 .

[25]  Randal E. Bryant,et al.  Symbolic Boolean manipulation with ordered binary-decision diagrams , 1992, CSUR.

[26]  Martin Gebser,et al.  Answer Set Solving in Practice , 2012, Answer Set Solving in Practice.

[27]  Adrian Walker,et al.  Towards a Theory of Declarative Knowledge , 1988, Foundations of Deductive Databases and Logic Programming..

[28]  Chiaki Sakama,et al.  Oscillating Behavior of Logic Programs , 2012, Correct Reasoning.

[29]  Laurent Simon,et al.  Efficient Consequence Finding , 2001, IJCAI.