Learning, Generalization, and Functional Entropy in Random Automata Networks

It has been shown \citep{broeck90:physicalreview,patarnello87:europhys} that feedforward Boolean networks can learn to perform specific simple tasks and generalize well if only a subset of the learning examples is provided for learning. Here, we extend this body of work and show experimentally that random Boolean networks (RBNs), where both the interconnections and the Boolean transfer functions are chosen at random initially, can be evolved by using a state-topology evolution to solve simple tasks. We measure the learning and generalization performance, investigate the influence of the average node connectivity $K$, the system size $N$, and introduce a new measure that allows to better describe the network's learning and generalization behavior. We show that the connectivity of the maximum entropy networks scales as a power-law of the system size $N$. Our results show that networks with higher average connectivity $K$ (supercritical) achieve higher memorization and partial generalization. However, near critical connectivity, the networks show a higher perfect generalization on the even-odd task

Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review

The paper characterizes classes of functions for which deep learning can be exponentially better than shallow learning. Deep convolutional networks are a special case of these conditions, though weight sharing is not the main reason for their exponential advantage

Verification of integer multipliers on the arithmetic bit level

One of the most severe short-comings of currently available equivalence checkers is their inability to verify integer multipliers. In this paper, we present a bit level reverse-engineering technique that can be integrated into standard equivalence checking flows. We propose a Boolean mapping algorithm that extracts a network of half adders from the gate netlist of an addition circuit. Once the arithmetic bit level representation of the circuit is obtained, equivalence checking can be performed using simple arithmetic operations. Experimental results show the promise of our approach

Fault-tolerance techniques for hybrid CMOS/nanoarchitecture

The authors propose two fault-tolerance techniques for hybrid CMOS/nanoarchitecture implementing logic functions as look-up tables. The authors compare the efficiency of the proposed techniques with recently reported methods that use single coding schemes in tolerating high fault rates in nanoscale fabrics. Both proposed techniques are based on error correcting codes to tackle different fault rates. In the first technique, the authors implement a combined two-dimensional coding scheme using Hamming and Bose-Chaudhuri-Hocquenghem (BCH) codes to address fault rates greater than 5. In the second technique, Hamming coding is complemented with bad line exclusion technique to tolerate fault rates higher than the first proposed technique (up to 20). The authors have also estimated the improvement that can be achieved in the circuit reliability in the presence of Don-t Care Conditions. The area, latency and energy costs of the proposed techniques were also estimated in the CMOS domain

Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table

Technology Mapping for Circuit Optimization Using Content-Addressable Memory

The growing complexity of Field Programmable Gate Arrays (FPGA's) is leading to architectures with high input cardinality look-up tables (LUT's). This thesis describes a methodology for area-minimizing technology mapping for combinational logic, specifically designed for such FPGA architectures. This methodology, called LURU, leverages the parallel search capabilities of Content-Addressable Memories (CAM's) to outperform traditional mapping algorithms in both execution time and quality of results. The LURU algorithm is fundamentally different from other techniques for technology mapping in that LURU uses textual string representations of circuit topology in order to efficiently store and search for circuit patterns in a CAM. A circuit is mapped to the target LUT technology using both exact and inexact string matching techniques. Common subcircuit expressions (CSE's) are also identified and used for architectural optimization---a small set of CSE's is shown to effectively cover an average of 96% of the test circuits. LURU was tested with the ISCAS'85 suite of combinational benchmark circuits and compared with the mapping algorithms FlowMap and CutMap. The area reduction shown by LURU is, on average, 20% better compared to FlowMap and CutMap. The asymptotic runtime complexity of LURU is shown to be better than that of both FlowMap and CutMap

OPTIMAL AREA AND PERFORMANCE MAPPING OF K-LUT BASED FPGAS

FPGA circuits are increasingly used in many fields: for rapid prototyping of new products (including fast ASIC implementation), for logic emulation, for producing a small number of a device, or if a device should be reconfigurable in use (reconfigurable computing). Determining if an arbitrary, given wide, function can be implemented by a programmable logic block, unfortunately, it is generally, a very difficult problem. This problem is called the Boolean matching problem. This paper introduces a new implemented algorithm able to map, both for area and performance, combinational networks using k-LUT based FPGAs.k-LUT based FPGAs, combinational circuits, performance-driven mapping.

Template-based embedded reconfigurable computing

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