8,025 research outputs found
Immunity and Simplicity for Exact Counting and Other Counting Classes
Ko [RAIRO 24, 1990] and Bruschi [TCS 102, 1992] showed that in some
relativized world, PSPACE (in fact, ParityP) contains a set that is immune to
the polynomial hierarchy (PH). In this paper, we study and settle the question
of (relativized) separations with immunity for PH and the counting classes PP,
C_{=}P, and ParityP in all possible pairwise combinations. Our main result is
that there is an oracle A relative to which C_{=}P contains a set that is
immune to BPP^{ParityP}. In particular, this C_{=}P^A set is immune to PH^{A}
and ParityP^{A}. Strengthening results of Tor\'{a}n [J.ACM 38, 1991] and Green
[IPL 37, 1991], we also show that, in suitable relativizations, NP contains a
C_{=}P-immune set, and ParityP contains a PP^{PH}-immune set. This implies the
existence of a C_{=}P^{B}-simple set for some oracle B, which extends results
of Balc\'{a}zar et al. [SIAM J.Comp. 14, 1985; RAIRO 22, 1988] and provides the
first example of a simple set in a class not known to be contained in PH. Our
proof technique requires a circuit lower bound for ``exact counting'' that is
derived from Razborov's [Mat. Zametki 41, 1987] lower bound for majority.Comment: 20 page
On unbalanced Boolean functions with best correlation immunity
It is known that the order of correlation immunity of a nonconstant
unbalanced Boolean function in variables cannot exceed ; moreover,
it is if and only if the function corresponds to an equitable
-partition of the -cube with an eigenvalue of the quotient matrix.
The known series of such functions have proportion , , or of
the number of ones and zeros. We prove that if a nonconstant unbalanced Boolean
function attains the correlation-immunity bound and has ratio of the
number of ones and zeros, then is divisible by . In particular, this
proves the nonexistence of equitable partitions for an infinite series of
putative quotient matrices. We also establish that there are exactly
equivalence classes of the equitable partitions of the -cube with quotient
matrix and classes, with . These
parameters correspond to the Boolean functions in variables with
correlation immunity and proportion and , respectively (the case
remains unsolved). This also implies the characterization of the
orthogonal arrays OA and OA.Comment: v3: final; title changed; revised; OA(512,11,2,6) discusse
Computation of epidemic final size distributions
We develop a new methodology for the efficient computation of epidemic final
size distributions for a broad class of Markovian models. We exploit a
particular representation of the stochastic epidemic process to derive a method
which is both computationally efficient and numerically stable. The algorithms
we present are also physically transparent and so allow us to extend this
method from the basic SIR model to a model with a phase-type infectious period
and another with waning immunity. The underlying theory is applicable to many
Markovian models where we wish to efficiently calculate hitting probabilities.Comment: final published versio
A Second Step Towards Complexity-Theoretic Analogs of Rice's Theorem
Rice's Theorem states that every nontrivial language property of the
recursively enumerable sets is undecidable. Borchert and Stephan initiated the
search for complexity-theoretic analogs of Rice's Theorem. In particular, they
proved that every nontrivial counting property of circuits is UP-hard, and that
a number of closely related problems are SPP-hard.
The present paper studies whether their UP-hardness result itself can be
improved to SPP-hardness. We show that their UP-hardness result cannot be
strengthened to SPP-hardness unless unlikely complexity class containments
hold. Nonetheless, we prove that every P-constructibly bi-infinite counting
property of circuits is SPP-hard. We also raise their general lower bound from
unambiguous nondeterminism to constant-ambiguity nondeterminism.Comment: 14 pages. To appear in Theoretical Computer Scienc
Resource Bounded Immunity and Simplicity
Revisiting the thirty years-old notions of resource-bounded immunity and
simplicity, we investigate the structural characteristics of various immunity
notions: strong immunity, almost immunity, and hyperimmunity as well as their
corresponding simplicity notions. We also study limited immunity and
simplicity, called k-immunity and feasible k-immunity, and their simplicity
notions. Finally, we propose the k-immune hypothesis as a working hypothesis
that guarantees the existence of simple sets in NP.Comment: This is a complete version of the conference paper that appeared in
the Proceedings of the 3rd IFIP International Conference on Theoretical
Computer Science, Kluwer Academic Publishers, pp.81-95, Toulouse, France,
August 23-26, 200
Complexity of certificates, heuristics, and counting types , with applications to cryptography and circuit theory
In dieser Habilitationsschrift werden Struktur und Eigenschaften von KomplexitÀtsklassen wie P und NP untersucht, vor allem im Hinblick auf: ZertifikatkomplexitÀt, Einwegfunktionen, Heuristiken gegen NP-VollstÀndigkeit und ZÀhlkomplexitÀt. Zum letzten Punkt werden speziell untersucht: (a) die KomplexitÀt von ZÀhleigenschaften von Schaltkreisen, (b) Separationen von ZÀhlklassen mit ImmunitÀt und (c) die KomplexitÀt des ZÀhlens der Lösungen von ,,tally`` NP-Problemen
Paths to a malaria vaccine illuminated by parasite genomics.
More human death and disease is caused by malaria parasites than by all other eukaryotic pathogens combined. As early as the sequencing of the first human genome, malaria parasite genomics was prioritized to fuel the discovery of vaccine candidate antigens. This stimulated increased research on malaria, generating new understanding of the cellular and molecular mechanisms of infection and immunity. This review of recent developments illustrates how new approaches in parasite genomics, and increasingly large amounts of data from population studies, are helping to identify antigens that are promising lead targets. Although these results have been encouraging, effective discovery and characterization need to be coupled with more innovation and funding to translate findings into newly designed vaccine products for clinical trials
- âŠ