In this paper we work with two canonical computational problems related to synchronization (SYN) and road coloring (SRCP).
Parameters: k, [absolute value of], t = [absolute value of I] SRCP Input: Alphabet I, admissible graph G = (Q, E) with out-degrees [absolute value of I], k [member of] N Output: Is there a coloring [delta] such that [absolute value of [delta](Q, w)] = 1 for some w [member of] [I.sup.*] of length at most k?
This means that the multi-parameter analysis of SYN and SRCP is complete in the sense that NP-complete restrictions are identified and we know, under several standard assumptions, which parameterizations lie in FPT and which of them have polynomial kernels.
We point out that SRCP parameterized by the number of states has a polynomial kernel, so it necessarily lies in FPT.
Proof: The algorithm takes an instance of SRCP, i.e., an alphabet I, an admissible graph G = (Q, E) with out-degrees |I|, and a number k [member of] N.
(I, G, k) [member of] SRCP [up down arrow] (I', G', k') [member of] SRCP.
Here we prove that SRCP restricted to |I| = 2 and k = 3 is decidable in polynomial time.
Additional information about Million Hearts, SRCP
, and CDC's Healthy Community Programs is available at http://millionhearts.hhs.gov and http://www.cdc.gov/nccdphp/dch/programs/healthycommunitiesprogram/index.htm.
Not only the SSQ and SRCP, but the entire process of recent internationalization of the religion-science discourse owes its existence and propagation to one funding source: the John Templeton Foundation.
It must be emphasized, however, that though both the SSQ and the SRCP were funded by the John Templeton Foundation, they were administered by the Center for Theology and the Natural Sciences (CTNS), a center that has a long-standing history of academic research and support for science and religion dialogue, and the foregoing remarks are not in any way meant to suggest any collusion between the John Templeton Foundation and CTNS.
It was therefore, natural that both SSQ and SRCP laid out a particularly Christian banquet, as it were, and invited the representatives of the other two Abrahamic traditions to partake of what was laid out.
highlights our goals, initiatives, and accomplishments in three major areas.