44,671 research outputs found
Dichotomy Results for Fixed Point Counting in Boolean Dynamical Systems
We present dichotomy theorems regarding the computational complexity of
counting fixed points in boolean (discrete) dynamical systems, i.e., finite
discrete dynamical systems over the domain {0,1}. For a class F of boolean
functions and a class G of graphs, an (F,G)-system is a boolean dynamical
system with local transitions functions lying in F and graphs in G. We show
that, if local transition functions are given by lookup tables, then the
following complexity classification holds: Let F be a class of boolean
functions closed under superposition and let G be a graph class closed under
taking minors. If F contains all min-functions, all max-functions, or all
self-dual and monotone functions, and G contains all planar graphs, then it is
#P-complete to compute the number of fixed points in an (F,G)-system; otherwise
it is computable in polynomial time. We also prove a dichotomy theorem for the
case that local transition functions are given by formulas (over logical
bases). This theorem has a significantly more complicated structure than the
theorem for lookup tables. A corresponding theorem for boolean circuits
coincides with the theorem for formulas.Comment: 16 pages, extended abstract presented at 10th Italian Conference on
Theoretical Computer Science (ICTCS'2007
One-dimensional fragment of first-order logic
We introduce a novel decidable fragment of first-order logic. The fragment is
one-dimensional in the sense that quantification is limited to applications of
blocks of existential (universal) quantifiers such that at most one variable
remains free in the quantified formula. The fragment is closed under Boolean
operations, but additional restrictions (called uniformity conditions) apply to
combinations of atomic formulae with two or more variables. We argue that the
notions of one-dimensionality and uniformity together offer a novel perspective
on the robust decidability of modal logics. We also establish that minor
modifications to the restrictions of the syntax of the one-dimensional fragment
lead to undecidable formalisms. Namely, the two-dimensional and non-uniform
one-dimensional fragments are shown undecidable. Finally, we prove that with
regard to expressivity, the one-dimensional fragment is incomparable with both
the guarded negation fragment and two-variable logic with counting. Our proof
of the decidability of the one-dimensional fragment is based on a technique
involving a direct reduction to the monadic class of first-order logic. The
novel technique is itself of an independent mathematical interest
Just how difficult can it be counting up R&D funding for emerging technologies (and is tech mining with proxy measures going to be any better?)
Decision makers considering policy or strategy related to the development of emerging technologies expect high quality data on the support for different technological options. A natural starting point would be R&D funding statistics. This paper explores the limitations of such aggregated data in relation to the substance and quantification of funding for emerging technologies.
Using biotechnology as an illustrative case, we test the utility of a novel taxonomy to demonstrate the endemic weaknesses in the availability and quality of data from public and private sources. Using the same taxonomy, we consider the extent to which tech-mining presents an alternative, or potentially complementary, way to determine support for emerging technologies using proxy measures such as patents and scientific publications
Counting occurrences of some subword patterns
We find generating functions the number of strings (words) containing a
specified number of occurrences of certain types of order-isomorphic classes of
substrings called subword patterns. In particular, we find generating functions
for the number of strings containing a specified number of occurrences of a
given 3-letter subword pattern.Comment: 9 page
Dichotomy Results for Fixed-Point Existence Problems for Boolean Dynamical Systems
A complete classification of the computational complexity of the fixed-point
existence problem for boolean dynamical systems, i.e., finite discrete
dynamical systems over the domain {0, 1}, is presented. For function classes F
and graph classes G, an (F, G)-system is a boolean dynamical system such that
all local transition functions lie in F and the underlying graph lies in G. Let
F be a class of boolean functions which is closed under composition and let G
be a class of graphs which is closed under taking minors. The following
dichotomy theorems are shown: (1) If F contains the self-dual functions and G
contains the planar graphs then the fixed-point existence problem for (F,
G)-systems with local transition function given by truth-tables is NP-complete;
otherwise, it is decidable in polynomial time. (2) If F contains the self-dual
functions and G contains the graphs having vertex covers of size one then the
fixed-point existence problem for (F, G)-systems with local transition function
given by formulas or circuits is NP-complete; otherwise, it is decidable in
polynomial time.Comment: 17 pages; this version corrects an error/typo in the 2008/01/24
versio
Tensor network method for reversible classical computation
We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.We thank Justin Reyes, Oskar Pfeffer, and Lei Zhang for many useful discussions. The computations were carried out at Boston University's Shared Computing Cluster. We acknowledge the Condensed Matter Theory Visitors Program at Boston University for support. Z.-C. Y. and C. C. are supported by DOE Grant No. DE-FG02-06ER46316. E.R.M. is supported by NSF Grant No. CCF-1525943. (Condensed Matter Theory Visitors Program at Boston University; DE-FG02-06ER46316 - DOE; CCF-1525943 - NSF)Accepted manuscrip
Software-based fault-tolerant routing algorithm in multidimensional networks
Massively parallel computing systems are being built with hundreds or thousands of components such as nodes, links, memories, and connectors. The failure of a component in such systems will not only reduce the computational power but also alter the network's topology. The software-based fault-tolerant routing algorithm is a popular routing to achieve fault-tolerance capability in networks. This algorithm is initially proposed only for two dimensional networks (Suh et al., 2000). Since, higher dimensional networks have been widely employed in many contemporary massively parallel systems; this paper proposes an approach to extend this routing scheme to these indispensable higher dimensional networks. Deadlock and livelock freedom and the performance of presented algorithm, have been investigated for networks with different dimensionality and various fault regions. Furthermore, performance results have been presented through simulation experiments
The number of clones determined by disjunctions of unary relations
We consider finitary relations (also known as crosses) that are definable via
finite disjunctions of unary relations, i.e. subsets, taken from a fixed finite
parameter set . We prove that whenever contains at least one
non-empty relation distinct from the full carrier set, there is a countably
infinite number of polymorphism clones determined by relations that are
disjunctively definable from . Finally, we extend our result to
finitely related polymorphism clones and countably infinite sets .Comment: manuscript to be published in Theory of Computing System
Does refusal bias influence the measurement of Chinese political trust?
Measurements of Chinese political trust may be inaccurate due to ‘refusal bias’, resulting from unwillingness of people with certain attitudes to take part in surveys. Such bias is especially problematic because researchers usually have little or no information about refusers. Nevertheless, techniques have been developed which allow correction of refusal bias by extrapolating from reluctant or difficult respondents on the basis of various measures of response propensity. Using data from a nationwide survey conducted in China in the winter of 2012/13, this article shows that this type of correction procedure improves the accuracy of measurement of the Communist Party membership rate, and produces significantly lower estimates of trust in the central government/Party leadership, trust in local government and support for the current system of government. Refusal bias is likely to result from the social desirability of expressing political trust and support under authoritarian conditions
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