In this paper, we are interested in memoryless computation, a modern paradigm to compute functions which generalises the famous XOR swap algorithm to exchange the contents of two variables without using a buffer. In m...
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In this paper, we are interested in memoryless computation, a modern paradigm to compute functions which generalises the famous XOR swap algorithm to exchange the contents of two variables without using a buffer. In memoryless computation, programs are only allowed to update one variable at a time. We first consider programs which do not use any memory. We study the maximum and average number of updates required to compute functions without memory. We then derive the exact number of instructions required to compute any manipulation of variables. This shows that combining variables, instead of simply moving them around, not only allows for memoryless programs, but also yields shorter programs. Second, we show that allowing programs to use memory is also incorporated in the memoryless computation framework. We then quantify the gains obtained by using memory: this leads to shorter programs and allows us to use only binary instructions, which is not sufficient in general when no memory is used. (C) 2014 Elsevier B.V. All rights reserved.
Consider a finite set A and n >= 1. We study complete simulation of transformations of A(n), also known as automata networks. For m >= n, a transformation of A(m) is n-complete of size m if it may simulate every...
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Consider a finite set A and n >= 1. We study complete simulation of transformations of A(n), also known as automata networks. For m >= n, a transformation of A(m) is n-complete of size m if it may simulate every transformation of A(n) by updating one register at a time. Using tools from memoryless computation, we establish that there is no n-complete transformation of size n, but there is one of size n + 1. By studying various constructions, we conjecture that the maximal time of simulation of any n-complete transformation is at least 2n. We also investigate the time and size of sequentially n-complete transformations, which may simulate every finite sequence of transformations of A(n). Finally, we show that there is no n-complete transformation updating all registers in parallel, but there exists one updating all but one register in parallel. This illustrates the strengths and weaknesses of sequential and parallel models of computation. (C) 2019 Elsevier Inc. All rights reserved.
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