Relational Approach to Boolean Logic Problems

  • Rudolf Berghammer
  • Ulf Milanese
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3929)


We present a method for specifying and implementing algorithms for Boolean logic problems. It is formally grounded in relational algebra. Specifications are written in first-order set theory and then transformed systematically into relation-algebraic forms which can be executed directly in RelView, a computer system for the manipulation of relations and relational programming. Our method yields programs that are correct by construction. It is illustrated by some examples.


Relational Approach Relational Algebra Conjunctive Normal Form Boolean Formula Binary Decision Diagram 
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  1. 1.
    Asahiro, Y., Iwama, K., Miyano, E.: Random generation of test instances with controlled attributes. In: Johnson, D.S., Trick, M.A. (eds.) Cliques, Coloring, and Satisfiability: The Second DIMACS Implementation Challenge. DIMACS Series on Discr. Math. and Theoret. Comput. Sci. vol. 26, pp. 377–394 (1996)Google Scholar
  2. 2.
    Behnke, R., et al.: RelView — A system for calculation with relations and relational programming. In: Astesiano, E. (ed.) ETAPS 1998 and FASE 1998. LNCS, vol. 1382, pp. 318–321. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  3. 3.
    Bryant, R.E.: Symbolic Boolean manipulation with ordered binary decision diagrams. ACM Comp. Surveys 24, 293–318 (1992)CrossRefGoogle Scholar
  4. 4.
    Crawford, J.M., Auton, L.D.: Experimental results on the crossover point in random 3SAT. Artificial Intelligence 81, 59–80 (1996)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Dantsin, E., Hirsch, E.A.: Algorithms for SAT and upper bounds of their complexity. Electr. Coll. Comp. Compl., Rep. 12 (2001),
  6. 6.
    Hoos, H.H., Stützle, T.: SATLIB: An online resource for research on Sat. In: Gent, I.P., van Maaren, H., Walsh, T. (eds.) SAT 2000, pp. 283–292. IOS Press, Amsterdam (2000)Google Scholar
  7. 7.
    Hromkovic, J.: Algorithms for hard problems. In: Introduction to combinatorial optimization, randomization, approximation, and heuristics. EATCS Texts in Theoret. Comput. Sci., Springer, Heidelberg (2001)Google Scholar
  8. 8.
    Huth, M.R.A., Ryan, M.D.: Logic in computer science. Cambr. Univ. Press (2000)Google Scholar
  9. 9.
    Leoniuk, B.: ROBDD-based implementation of relational algebra with applications (in German). Ph.D. thesis, Inst. für Inf. und Prak. Math., Univ. Kiel (2001)Google Scholar
  10. 10.
    Lind-Nielson, J.: BuDDy, a binary decision diagram package, version 2.2. Techn. Univ. of Denmark (2003),
  11. 11.
    Milanese, U.: On the implementation of a ROBDD-based tool for the manipulation and visualization of relations (in German). Ph.D. thesis, Inst. für Inf. und Prak. Math., Univ. Kiel (2003)Google Scholar
  12. 12.
    Purdam, P.: A survey of average time analysis of satisfiability algorithms. J. of Inf. Processing 13, 449–455 (1990)Google Scholar
  13. 13.
    Schmidt, G., Ströhlein, T.: Relations and graphs. In: Discrete Mathematics for Computer Scientists. EATCS Monographs on Theoret. Comput. Sci., Springer, Heidelberg (1993)Google Scholar
  14. 14.
    Somenzi, F.: CUDD: CU decision diagram package, release 2.3.1. Univ. of Colorado at Boulder (2001),
  15. 15.
    Tarski, A.: On the calculus of relations. J. Symbolic Logic 6, 73–89 (1941)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Rudolf Berghammer
    • 1
  • Ulf Milanese
    • 1
  1. 1.Institut für Informatik und Praktische MathematikUniversität KielKielGermany

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