Abstract
In this paper we introduce a Prover-Verifier model for analyzing the computational complexity of a class of Constraint Satisfaction problems termed Binary Boolean Constraint Satisfaction problems (BBCSPs). BBCSPs represent an extremely general class of constraint satisfaction problems and find applications in a wide variety of domains including constraint programming, puzzle solving and program testing. We establish that each instance of a BBCSP admits a coin-flipping Turing Machine that halts in time polynomial in the size of the input. The prover P in the Prover-Verifier model is endowed with very limited powers; in particular, it has no memory and it can only pose restricted queries to the verifier. The verifier on the other hand is both omniscient in that it is cognizant of all the problem details and insincere in that it does not have to decide a priori on the intended proof. However, the verifier must stay consistent in its responses. Inasmuch as our provers will be memoryless and our verifiers will be asked for extremely simple certificates, our work establishes the existence of a simple, randomized algorithm for BBCSPs. Our model itself serves as a basis for the design of zero-knowledge machine learning algorithms in that the prover ends up learning the proof desired by the verifier.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aiken, A.: Introduction to set constraint-based program analysis. Science of Computer Programming 35(2), 79–111 (1999)
Aspvall, B., Plass, M.F., Tarjan, R.: A linear-time algorithm for testing the truth of certain quantified boolean formulas. Information Processing Letters 8(3), 121–123 (1979)
de Moura, L.M., Owre, S., Ruess, H., Rushby, J.M., Shankar, N.: The ics decision procedures for embedded deduction. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, pp. 218–222. Springer, Heidelberg (2004)
Karger, D.R., Klein, P.N., Tarjan, R.E.: A randomized linear-time algorithm to find minimum spanning trees. Journal of the ACM 42(2), 321–328 (1995)
Khachiyan, L.G.: A polynomial algorithm for linear programming. Soviet Math. Doklady, vol. 20, pp. 191–194 (1979) (Russian original in Doklady Akademiia Nauk SSSR 244, 1093–1096)
Marriott, K., Stuckey, P.J.: Programming with Constraints: An Introduction. The MIT Press, Cambridge (1998)
Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, Cambridge, England (1995)
Papadimitriou, C.H.: On selecting a satisfying truth assignment. In: IEEE (ed.), Proceedings: 32nd annual Symposium on Foundations of Computer Science, San Juan, Puerto Rico, pp. 163–169, October 1–4 (1991), 1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA. IEEE Computer Society Press, Los Alamitos (1991)
Ross, S.M.: Probability Models, 7th edn. Academic Press, Inc., San Diego (2000)
Schlenker, H., Rehberger, F.: Towards a more general distributed constraint satisfaction framework: Intensional vs. extensional constraint representation. In: 15. WLP, pp. 63–70 (2000)
Schöning, U.: New algorithms for k-SAT based on the local search principle. In: MFCS: Symposium on Mathematical Foundations of Computer Science (2001)
Sheini, H.M., Sakallah, K.A.: From propositional satisfiability to satisfiability modulo theories. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 1–9. Springer, Heidelberg (2006)
Subramani, K.: An analysis of zero-clairvoyant scheduling. In: Katoen, J.-P., Stevens, P. (eds.) ETAPS 2002 and TACAS 2002. LNCS, vol. 2280, pp. 98–112. Springer, Heidelberg (2002)
Subramani, K.: An analysis of totally clairvoyant scheduling. Journal of Scheduling 8(2), 113–133 (2005)
Subramani, K.: Cascading random walks. International Journal of Foundations of Computer Science (IJFCS) 16(3), 599–622 (2005)
Subramani, K.: Totally clairvoyant scheduling with relative timing constraints. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 398–411. Springer, Heidelberg (2005)
Valiant, L.G.: A theory of the learnable. Communications of the ACM 27(11), 1134–1142 (1984)
Wei, W., Selman, B.: Accelerating random walks. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 216–232. Springer, Heidelberg (2002)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Subramani, K. (2007). A Randomized Algorithm for BBCSPs in the Prover-Verifier Model. In: Jones, C.B., Liu, Z., Woodcock, J. (eds) Theoretical Aspects of Computing – ICTAC 2007. ICTAC 2007. Lecture Notes in Computer Science, vol 4711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75292-9_31
Download citation
DOI: https://doi.org/10.1007/978-3-540-75292-9_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75290-5
Online ISBN: 978-3-540-75292-9
eBook Packages: Computer ScienceComputer Science (R0)