منابع مشابه
Arithmetic Design for Permutation Groups
This paper investigates the hardware implementation of arithmetical operations (multiplication and inversion) in symmetric and alternating groups, as well as in binary permutation groups (permutation groups of order 2). Various fast and space-efficient hardware architectures will be presented. High speed is achieved by employing switching networks, which effect multiplication in one clock cycle...
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First order reasoning about hyperintegers can prove things about sets of integers. In the author’s paper Nonstandard Arithmetic and Reverse Mathematics, Bulletin of Symbolic Logic 12 (2006), it was shown that each of the “big five” theories in reverse mathematics, including the base theory RCA0, has a natural nonstandard counterpart. But the counterpart RCA0 of RCA0 has a defect: it does not im...
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Interpretations are a natural tool in comparing the strength of two theories. In this paper we give a brief introduction to the topic of interpretability and interpretability logics. We will focus on the, so far, unknown interpretability logic of PRA. One research technique will be treated. This technique can be best described as restricting the realizations in the arithmetical semantics. 1 Wha...
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We propose a new fixed precision arithmetic package called RecInt. It uses a recursive double-size data-structure. Contrary to arbitrary precision packages like GMP, that create vectors of words on the heap, RecInt large integers are created on the stack. The space allocated for these integers is a power of two and arithmetic is performed modulo that power. Operations are thus easily implemente...
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N-chain recursions are important because the majority of single-linear recursions can be compiled to N-chain recursions or so-called bounded recursions [8], which are not recursive at all. It appeared for some time [3, 5] that ALL single linear recursions could be converted to N-chain recursions. Although that is now known [13] to be inaccurate it is still clear that the most popular forms of S...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1953
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-10380