Automatic Generation of Implied Constraints

A well-known difficulty with solving Constraint Satisfaction Problems (CSPs) is that, while one formulation of a CSP may enable a solver to solve it quickly, a different formulation may take prohibitively long to solve. We demonstrate a system for automatically reformulating CSP solver models by combining the capabilities of machine learning and automated theorem proving with CSP systems. Our system is given a basic CSP formulation and outputs a set of reformulations, each of which includes additional constraints. The additional constraints are generated through a machine learning process and are proven to follow from the basic formulation by a theorem prover. Experimenting with benchmark problem classes from finite algebras, we show how the time invested in reformulation is often recovered many times over when searching for solutions to more difficult problems from the problem class.

[1]  Contents , 2003 .

[2]  S. Colton,et al.  Expressing General Problems as CSPs , 2006 .

[3]  Simon Colton,et al.  Constraint Generation via Automated Theory Formation , 2001, CP.

[4]  Barry O'Sullivan,et al.  A SAT-Based Version Space Algorithm for Acquiring Constraint Satisfaction Problems , 2005, ECML.

[5]  Peter J. Stuckey,et al.  Programming with Constraints: An Introduction , 1998 .

[6]  Christian Bessiere,et al.  Acquiring Parameters of Implied Global Constraints , 2005, CP.

[7]  Rina Dechter,et al.  Resolution versus Search: Two Strategies for SAT , 2000, Journal of Automated Reasoning.

[8]  Mark Wallace,et al.  Practical applications of constraint programming , 2004, Constraints.

[9]  Toby Walsh,et al.  CGRASS: A System for Transforming Constraint Satisfaction Problems , 2002, International Workshop on Constraint Solving and Constraint Logic Programming.

[10]  Joao Marques-Silva,et al.  Conflict analysis in search algorithms for satisfiability , 1996, Proceedings Eighth IEEE International Conference on Tools with Artificial Intelligence.

[11]  Mats Carlsson,et al.  An Open-Ended Finite Domain Constraint Solver , 1997, PLILP.

[12]  Byungki Cha,et al.  Adding New Clauses for Faster Local Search , 1996, AAAI/IAAI, Vol. 1.

[13]  Barry O'Sullivan,et al.  Leveraging the Learning Power of Examples in Automated Constraint Acquisition , 2004, CP.

[14]  Meinolf Sellmann,et al.  Streamlined Constraint Reasoning , 2004, CP.

[15]  Toby Walsh,et al.  Modelling the Golomb Ruler Problem , 1999 .

[16]  Eugene C. Freuder,et al.  Using Case-Based Reasoning to Write Constraint Programs , 2003, CP.

[17]  Toby Walsh,et al.  Automatic Concept Formation in Pure Mathematics , 1999, IJCAI.

[18]  Cormac Gebruers,et al.  Capturing Constraint Programming Experience: A Case-Based Approach , 2002 .

[19]  Alan Bundy,et al.  A Science of Reasoning , 1991, Computational Logic - Essays in Honor of Alan Robinson.

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

[21]  Toby Walsh,et al.  The Use of Proof Plans to Sum Series , 1992, CADE.

[22]  Frank van Harmelen,et al.  Rippling: A Heuristic for Guiding Inductive Proofs , 1993, Artif. Intell..

[23]  Ronald Fagin.  Generalized first-order spectra, and polynomial. time recognizable sets , 1974 .

[24]  David A. Duffy,et al.  Principles of automated theorem proving , 1991, Wiley professional computing.

[25]  MSc PhD Simon Colton BSc.  Automated Theory Formation in Pure Mathematics , 2002, Distinguished Dissertations.