We study structural aspects of randomized parameterized computation. We introduce a new class W[P]-PFPT as a natural parameterized analogue of PP. Our definition uses the machine based characterization of the parameterized complexity class W[P] obtained by Chen et.al [TCS 2005]. We translate most of the structural properties and characterizations of the class PP to the new class W[P]-PFPT. We study a parameterization of the polynomial identity testing problem based on the degree of the polynomial computed by the arithmetic circuit. We obtain a parameterized analogue of the well known Schwartz-Zippel lemma [Schwartz, JACM 80 and Zippel, EUROSAM 79]. Additionally, we introduce a parameterized variant of permanent, and prove its #W[1] completeness.
CITATION STYLE
Chauhan, A., & Raghavendra Rao, B. V. (2015). Parameterized analogues of probabilistic computation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8959, pp. 181–192). Springer Verlag. https://doi.org/10.1007/978-3-319-14974-5_18
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