Constraint satisfaction problem

Not to be confused with Communicating sequential processes.

Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods. CSPs are the subject of research in both artificial intelligence and operations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families. CSPs often exhibit high complexity, requiring a combination of heuristics and combinatorial search methods to be solved in a reasonable time. Constraint programming (CP) is the field of research that specifically focuses on tackling these kinds of problems.[1][2] Additionally, the Boolean satisfiability problem (SAT), satisfiability modulo theories (SMT), mixed integer programming (MIP) and answer set programming (ASP) are all fields of research focusing on the resolution of particular forms of the constraint satisfaction problem.

Examples of problems that can be modeled as a constraint satisfaction problem include:

These are often provided with tutorials of CP, ASP, Boolean SAT and SMT solvers. In the general case, constraint problems can be much harder, and may not be expressible in some of these simpler systems. "Real life" examples include automated planning,[6][7] lexical disambiguation,[8][9] musicology,[10] product configuration[11] and resource allocation.[12]

The existence of a solution to a CSP can be viewed as a decision problem. This can be decided by finding a solution, or failing to find a solution after exhaustive search (stochastic algorithms typically never reach an exhaustive conclusion, while directed searches often do, on sufficiently small problems). In some cases the CSP might be known to have solutions beforehand, through some other mathematical inference process.

  1. ^ Lecoutre, Christophe (2013). Constraint Networks: Techniques and Algorithms. Wiley. p. 26. ISBN 978-1-118-61791-5.
  2. ^ "Constraints – incl. option to publish open access". springer.com. Retrieved 2019-10-03.
  3. ^ Chandra, Satish; Gordon, Colin S.; Jeannin, Jean-Baptiste; Schlesinger, Cole; Sridharan, Manu; Tip, Frank; Choi, Youngil (2016). "Type inference for static compilation of JavaScript" (PDF). Proceedings of the 2016 ACM SIGPLAN International Conference on Object-Oriented Programming, Systems, Languages, and Applications. pp. 410–429. doi:10.1145/2983990.2984017. ISBN 978-1-4503-4444-9.
  4. ^ Jim, Trevor, and Jens Palsberg. "Type inference in systems of recursive types with subtyping." Available on authors' web page (1999).
  5. ^ Farhi, Edward; Aram W Harrow (2016). "Quantum Supremacy through the Quantum Approximate Optimization Algorithm". arXiv:1602.07674 [quant-ph].
  6. ^ Malik Ghallab; Dana Nau; Paolo Traverso (21 May 2004). Automated Planning: Theory and Practice. Elsevier. pp. 1–. ISBN 978-0-08-049051-9.
  7. ^ Dynamic Flexible Constraint Satisfaction and Its Application to AI Planning, Archived 2009-02-06 at the Wayback Machine Ian Miguel – slides.
  8. ^ Demetriou, George C. "Lexical disambiguation using constraint handling in Prolog (CHIP)." Proceedings of the sixth conference on European chapter of the Association for Computational Linguistics. Association for Computational Linguistics, 1993.
  9. ^ MacDonald, Maryellen C., and Mark S. Seidenberg. "Constraint satisfaction accounts of lexical and sentence comprehension." Handbook of Psycholinguistics (Second Edition). 2006. 581–611.
  10. ^ Mauricio Toro, Carlos Agon, Camilo Rueda, Gerard Assayag. "GELISP: A FRAMEWORK TO REPRESENT MUSICAL CONSTRAINT SATISFACTION PROBLEMS AND SEARCH STRATEGIES." Journal of Theoretical and Applied Information Technology 86 (2). 2016. 327–331.
  11. ^ Applying constraint satisfaction approach to solve product configuration problems with cardinality-based configuration rules, Dong Yang & Ming Dong, Journal of Intelligent Manufacturing volume 24, pages99–111 (2013)
  12. ^ Modi, Pragnesh Jay, et al. "A dynamic distributed constraint satisfaction approach to resource allocation." International Conference on Principles and Practice of Constraint Programming. Springer, Berlin, Heidelberg, 2001.