کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6876045 | 690189 | 2015 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Real or natural number interpretation and their effect on complexity
ترجمه فارسی عنوان
تفسیر تعداد واقعی و یا طبیعی و تاثیر آن بر پیچیدگی
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کلمات کلیدی
پیچیدگی محاسباتی نامتجانس، دوره بازنویسی، تفسیر چندجملهای، هندسه جبری
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
چکیده انگلیسی
Interpretation methods have been introduced in the 70s by Lankford [1] in rewriting theory to prove termination. Actually, as shown by Bonfante et al. [2], an interpretation of a program induces a bound on its complexity. However, Lankford's original analysis depends deeply on the Archimedean property of natural numbers. This goes against the fact that finding a real interpretation can be solved by Tarski's decision procedure over the reals (as described by Dershowitz in [3]), and consequently interpretations are usually chosen over the reals rather than over the integers. Doing so, one cannot use anymore the (good) properties of the natural (well-)ordering of N used to bound the complexity of programs. We prove that one may take benefit from the best of both worlds: the complexity analysis still holds even with real numbers. The reason lies in a deep algebraic property of polynomials over the reals. We illustrate this by two characterizations, one of polynomial time and one of polynomial space.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Theoretical Computer Science - Volume 585, 20 June 2015, Pages 25-40
Journal: Theoretical Computer Science - Volume 585, 20 June 2015, Pages 25-40
نویسندگان
Guillaume Bonfante, Florian Deloup, Antoine Henrot,