For a word equation E of length n in one variable x occurring # (x) times in E a resolution algorithm of O(n+# (x) log n) time complexity is presented here. This is the best result known and for the equations that fea...
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For a word equation E of length n in one variable x occurring # (x) times in E a resolution algorithm of O(n+# (x) log n) time complexity is presented here. This is the best result known and for the equations that feature #(x) < n/logn it yields time complexity of O(n) which is optimal. Additionally it is proven here that the set of solutions of any one-variable word equation is either of the form F or of the form F boolean OR(uv)(+) u where F is a set of O(log n) words and u, v are some words such that uv is a primitive word.
Improving encoding and decoding time in compression technique is a great demand to modern users. In bit level compression technique, it requires more time to encode or decode every single bit when a binary code is use...
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Although computer architectures incorporate fast processing hardware resources, high performance real-time implementation of a complex control algorithm requires an efficient design and software coding of the algorith...
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Although computer architectures incorporate fast processing hardware resources, high performance real-time implementation of a complex control algorithm requires an efficient design and software coding of the algorithm so as to exploit special features of the hardware and avoid associated architecture shortcomings. This paper presents an investigation into the analysis and design mechanisms that will lead to reduction in the execution time in implementing real-time control algorithms. The proposed mechanisms are exemplified by means of one algorithm, which demonstrates their applicability to real-time applications. An active vibration control （AVC） algorithm for a flexible beam system simulated using the finite difference （FD） method is considered to demonstrate the effectiveness of the proposed methods. A comparative performance evaluation of the proposed design mechanisms is presented and discussed through a set of experiments.
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