J.T. Butler

Naval Postgraduate School, Monterey, California, United States

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Publications (9)2.01 Total impact

  • S. Nagayama · T. Sasao · J.T. Butler
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    ABSTRACT: A multi-state system with multi-state components is a model of systems, where performance, capacity, or reliability levels of the systems are represented as states. It usually has more than two states, and thus can be considered as a multi-valued function, called a structure function. Since many structure functions are monotone increasing, their multi-state systems can be represented compactly by edge-valued multivalued decision diagrams (EVMDDs). This paper presents an analysis method of multi-state systems with multi-state components using EVMDDs. Experimental results show that, by using EVMDDs, structure functions can be represented more compactly than existing methods using ordinary MDDs. Further, EVMDDs yield comparable computation time for system analysis. This paper also proposes a new diagnosis method using EVMDDs, and shows that the proposed method can infer the most probable causes for system failures more efficiently than conventional methods based on Bayesian networks.
    No preview · Article · Jan 2014 · Journal of multiple-valued logic and soft computing
  • Shinobu Nagayama · Tsutomu Sasao · J.T. Butler
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    ABSTRACT: This paper proposes an algorithm to minimize the number of edges in an edge-valued multi-valued decision diagram (EVMDD) for fast analysis of multi-state systems. We minimize the number of edges by grouping multi-valued variables into larger-valued variables. By grouping multi-valued variables, we can also reduce the number of nodes. However, minimization of the number of nodes by grouping variables is not always effective for fast analysis of multi-state systems. On the other hand, minimization of the number of edges is effective. Experimental results show that the proposed algorithm for minimizing the number of edges reduces the number of edges by up to 15% and the number of nodes by up to 47%. This results in a speed-up of the analysis of multi-state systems by about three times.
    No preview · Conference Paper · May 2013
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    J.T. Butler · T. Sasao
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    ABSTRACT: We demonstrate a circuit that generates a permutation in response to an index. Since there are n! n-element permutations, the index ranges from 0 to n! - 1. Such a circuit is needed in the hardware implementation of unique-permutation hash functions to specify how parallel machines interact through a shared memory. Such a circuit is also needed in cryptographic applications. The circuit is based on the factorial number system. Here, each non-negative integer is uniquely represented as sn-1(n - 1)! + sn-2(n - 2)! +. . . + s11!, where 1 ≤ si ≤ i. That is, the permutation is produced by generating the digits si in the factorial number system representation of the index. The circuit is combinational and is easily pipelined to produce one permutation per clock period. We give experimental results that show the efficiency of our designs. For example. we show that the rate of production of permutations on the SRC-6 reconfigurable computer is 1,820 times faster than a program on a conventional microprocessor in the case of 10-element permutations. We also show an efficient reconfigurable computer implementation that produces random permutations using the Knuth shuffle algorithm. This is useful in Monte Carlo simulations. For both circuits, the complexity is O(n2), and the delay is O(n).
    Preview · Conference Paper · Jan 2012
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    J T Butler · T Sasao · S Nagayama
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    ABSTRACT: We show the architecture and design of a numeric function generator that realizes, at high speed, arithmetic functions, like log x, sin x, 1 x , etc.. This approach is general; different circuits are not needed for different functions. Further, composite functions, like log (sin ( 1 x )) can be realized as easily as individual functions. A tutorial description of the method is presented, followed by descriptions of the design considerations that must be made. For example, we discuss how circuit complexity increases as the desired approximation error decreases. Also, we discuss enhancements of the basic numeric function generator approach, including higher order polynomial approximations, floating point, and multi-variable implementations.
    Full-text · Article · Jun 2009
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    T. Sasao · J.T. Butler · M. D. Riedel
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    ABSTRACT: The availability of large, inexpensive memory has made it possible to realize numerical functions, such as the reciprocal, square root, and trigonometric functions, using a lookup table. This is much faster than by software. However, a naive look-up method requires unreasonably large memory. In this paper, we show the use of a look-up table (LUT) cascade to realize a piecewise linear approximation to the given function. Our approach yields memory of reasonable size and significant accuracy.
    Preview · Article · Jul 2004
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    T Sasao · J T Butler · M Matsuura
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    ABSTRACT: This paper focuses on the average path length (APL) of BDD's for switching functions. APL is a metric for the time it takes to evaluate the function by a computer program. We derive the APL for the AND, OR, parity, carry-out, com-parison, threshold symmetric, and majority functions. We also consider the average of the APL for various classes of functions, including symmetric, threshold symmetric, and unate cascade. For symmetric functions, we show the average APL is close to the maximum path length, n, the number of variables. We show there are exactly two functions, the parity functions, that achieve the upper bound, n, on the APL for BDD's over all functions dependent on n variables. All other functions have an APL strictly less than n. We show that the APL of BDD's over all functions dependent on n variables is bounded below by 2 − 1 2 n−1 . The set of functions that achieves this small value is uniquely the set of unate cascade realizable functions. We also show that the APL for benchmark functions is typically much less than for random functions.
    Preview · Article · Dec 2002
  • T. Sasao · J.T. Butler
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    ABSTRACT: In an irredundant sum-of-products expression (ISOP), each product is a prime implicant (Pl) and no product can be deleted without changing the function. Among the ISOPs for some function f, a worst ISOP (WSOP) is an ISOP with the largest number of Pls and a minimum ISOP (MSOP) is one with the smallest number. We show a class of functions for which the Minato-Morreale ISOP algorithm produces WSOPs. Since the ratio of the size of the WSOP to the size of the MSOP is arbitrarily large when it, the number of variables, is unbounded, the Minato-Morreale algorithm can produce results that are very far from minimum. We present a class of multiple-output functions whose WSOP size is also much larger than its MSOP size. For a set of benchmark functions, we show the distribution of ISOPs to the number of Pls. Among this set are functions where the MSOPs have almost as many Pls as do the WSOPs. These functions are known to be easy to minimize. Also, there are benchmark functions where the fraction of ISOPs that are MSOPs is small and MSOPs have many fewer Pls than the WSOPs. Such functions are known to be hard to minimize. For one class of functions, we show that the fraction of ISOPs that are MSOPs approaches 0 as n approaches infinity, suggesting that such functions are hard to minimize
    No preview · Article · Sep 2001 · IEEE Transactions on Computers
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    T. Sasao · J.T. Butler
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    ABSTRACT: Multiple-output switching functions can be simulated by multiple-valued decision diagrams (MDDs) at a significant reduction in computation time. analyze the following approaches to the representation problem: shared multiple-valued decision diagrams (SMDDs), multi-terminal multiple-valued decision diagrams (MTMDDs), and shared multi-terminal multiple-valued decision diagrams(SMTMDDs). For example, we show that SMDDs fend to be compact, while SMTMDDs tend to be fast. We present an algorithm for grouping input variables and output functions in the MDDs
    Preview · Conference Paper · Jun 1996
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    T Sasao · J T Butler
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    ABSTRACT: We introduce eigenfunctions of the Reed-Muller trans-form. Eigenfunctions are functions whose canonical sum-of-products expression and PPRM (positive polarity Reed-Muller expression) are isomorphic. In the case of symmet-ric functions, the eigenfunction can be viewed as a function whose reduced truth vector is identical to the reduced Reed-Muller spectrum. We show that the number of symmetric (ordinary) eigenfunctions on Ò-variables is ¾ Ò·½ ¾ (¾ ¾ Ò½).
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