Abstract
We consider probability distributions which are associated with the running time of probabilistic algorithms, given for algorithmic processing in symbolic form. The considered decision (also counting) problems deal with the question whether a complete restart of the underlying probabilistic algorithm after some number of steps t gives an advantage. Since deciding whether a given symbolic formula indeed represents a probability distribution (either as probability mass function or as cumulative distribution function) is itself a difficult problem to decide, we discuss the issue in terms of promise problems.
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References
Even, S., Selman, A.L., Yacobi, Y.: The complexity of promise problems with applications to public-key cryptography. Inf. Control 61(2), 159–173 (1984)
Goldreich, O.: On promise problems: a survey. In: Goldreich, O., Rosenberg, A.L., Selman, A.L. (eds.) Theoretical Computer Science. LNCS, vol. 3895, pp. 254–290. Springer, Heidelberg (2006). https://doi.org/10.1007/11685654_12
Gomes, C.P., Selman, B., Kautz, H.: Boosting combinatorial search through randomization. In: National Conference on Artificial Intelligence, pp. 431–437. AAAI Press (1998)
Ko, K.: Complexity Theory of Real Functions. Birkhäuser, Boston (1991)
Köbler, J., Schöning, U., Torán, J.: The Graph Isomorphism Problem - Its Structural Complexity. Birkhäuser, Boston (1993)
Lorenz, J.-H.: On the complexity of restarting. In: van Bevern, R., Kucherov, G. (eds.) CSR 2019. LNCS, vol. 11532, pp. 250–261. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-19955-5_22
Luby, M., Sinclair, A., Zuckerman, D.: Optimal speed-up of las vegas algorithms. Inf. Process. Lett. 47(4), 173–180 (1993)
Schöning, U.: A probabilistic algorithm for k-SAT and constraint satisfaction problems. In: 40th Annual Symposium on Foundations of Computer Science, pp. 410–414. IEEE (1999)
Selman, A.L.: Promise problems complete for complexity classes. Inf. Comput. 78(2), 87–98 (1988)
Toda, S.: The complexity of finding medians. In: Proceedings 31th Annual Symposium on Foundations of Computer Science, pp. 778–787. IEEE (1990)
Toda, S.: PP is as hard as the polynomial-time hierarchy. SIAM J. Comput. 20, 865–877 (1991)
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Lorenz, JH., Schöning, U. (2020). Promise Problems on Probability Distributions. In: Du, DZ., Wang, J. (eds) Complexity and Approximation. Lecture Notes in Computer Science(), vol 12000. Springer, Cham. https://doi.org/10.1007/978-3-030-41672-0_5
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DOI: https://doi.org/10.1007/978-3-030-41672-0_5
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