116 research outputs found
Hopfield models as nondeterministic finite-state machines
The use of neural networks for integrated linguistic analysis may be profitable. This paper presents the first results of our research on that subject: a Hopfield model for syntactical analysis. We construct a neural network as an implementation of a bounded push-down automaton, which can accept context-free languages with limited center-embedding. The network's behavior can be predicted a priori, so the presented theory can be tested. The operation of the network as an implementation of the acceptor is provably correct. Furthermore we found a solution to the problem of spurious states in Hopfield models: we use them as dynamically constructed representations of sets of states of the implemented acceptor. The so-called neural-network acceptor we propose, is fast but large
On the Computational Power of DNA Annealing and Ligation
In [20] it was shown that the DNA primitives of Separate,
Merge, and Amplify were not sufficiently powerful to invert
functions defined by circuits in linear time. Dan Boneh et
al [4] show that the addition of a ligation primitive, Append, provides the missing power. The question becomes, "How powerful is ligation? Are Separate, Merge, and Amplify
necessary at all?" This paper proposes to informally explore
the power of annealing and ligation for DNA computation.
We conclude, in fact, that annealing and ligation alone are
theoretically capable of universal computation
Complexity of Restricted and Unrestricted Models of Molecular Computation
In [9] and [2] a formal model for molecular computing was
proposed, which makes focused use of affinity purification.
The use of PCR was suggested to expand the range of
feasible computations, resulting in a second model. In this
note, we give a precise characterization of these two models
in terms of recognized computational complexity classes,
namely branching programs (BP) and nondeterministic
branching programs (NBP) respectively. This allows us to
give upper and lower bounds on the complexity of desired
computations. Examples are given of computable and
uncomputable problems, given limited time
Computational Capabilities of Analog and Evolving Neural Networks over Infinite Input Streams
International audienceAnalog and evolving recurrent neural networks are super-Turing powerful. Here, we consider analog and evolving neural nets over infinite input streams. We then characterize the topological complexity of their ω-languages as a function of the specific analog or evolving weights that they employ. As a consequence, two infinite hierarchies of classes of analog and evolving neural networks based on the complexity of their underlying weights can be derived. These results constitute an optimal refinement of the super-Turing expressive power of analog and evolving neural networks. They show that analog and evolving neural nets represent natural models for oracle-based infinite computation
Convergence of Opinion Diffusion is PSPACE-complete
We analyse opinion diffusion in social networks, where a finite set of
individuals is connected in a directed graph and each simultaneously changes
their opinion to that of the majority of their influencers. We study the
algorithmic properties of the fixed-point behaviour of such networks, showing
that the problem of establishing whether individuals converge to stable
opinions is PSPACE-complete
Design of General Purpose Minimal-Auxiliary Ising Machines
Ising machines are a form of quantum-inspired processing-in-memory computer
which has shown great promise for overcoming the limitations of traditional
computing paradigms while operating at a fraction of the energy use. The
process of designing Ising machines is known as the reverse Ising problem.
Unfortunately, this problem is in general computationally intractable: it is a
nonconvex mixed-integer linear programming problem which cannot be naively
brute-forced except in the simplest cases due to exponential scaling of runtime
with number of spins. We prove new theoretical results which allow us to reduce
the search space to one with quadratic scaling. We utilize this theory to
develop general purpose algorithmic solutions to the reverse Ising problem. In
particular, we demonstrate Ising formulations of 3-bit and 4-bit integer
multiplication which use fewer total spins than previously known methods by a
factor of more than three. Our results increase the practicality of
implementing such circuits on modern Ising hardware, where spins are at a
premium.Comment: 14 pages, 3 figures, submitted to IEEE International Conference on
Rebooting Computing 202
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