محاسبه حد بالای سرعت انجام محاسبات و نرخ رشد پیچیدگی با استفاده از روش ریاضی نظریه اختلال
محورهای موضوعی : آمارحسین باقری 1 , محمدرضا تنهایی 2
1 - گروه فیزیک واحد تهران مرکزی دانشگاه آزاد اسلامی تهران ایران
2 - گروه فیزیک، واحد تهران مرکزی، دانشگاه آزاد اسلامی تهران ایران
کلید واژه: Disruption theory, synchronized oscillator, the complexity of performing calculations,
چکیده مقاله :
سرعت انجام محاسبه و میزان توانایی در انجام محاسبات برای یک سیستم محاسباتی دو سوال بنیادی در علوم رایانه می باشند همچنین مفهوم پیچیدگی انجام محاسبه به زبان ماشین و سنجه ای که برای پیچیدگی ارایه می شود، کمیت های مهمی هستند. در این مقاله، با استفاده از روش های ریاضی و به صورت مشخص با بهره جستن از نظریه اختلال، نرخ رشد پیچیدگی انجام محاسبات را برای یک نوسانگر ناهماهنگ محاسبه می کنیم. علت انتخاب نوسانگر به این دلیل است که اکثر سیستم های فیزیکی را می توان با نوسانگر شبیه سازی کرد. همچنین حداکثر تحول دینامیکی حالت های کوانتومی را که میزان محاسبه را تغییر می دهد، محاسبه می کنیم و به عنوان دستاورد مهم این کار نشان می دهیم که برای اختلال مرتبه زوج، میزان پیچیدگی افزایش می یابد، در حالی که برای اختلال مرتبه فرد نرخ، رفتار کاهشی خواهیم داشت. این روش می تواند الگوی نظری برای حد بالای انجام محاسبات در نظر گرفته شود.
The speed of calculation and the level of ability to perform calculations for a computing system are two fundamental questions in computer science. Also, the concept of complexity of performing calculations in machine language and the measure provided for complexity are important quantities. In this article, we calculate the growth rate of the complexity of performing calculations for an asynchronous oscillator by using mathematical methods and specifically using the disturbance theory. The reason for choosing an oscillator is that most physical systems can be simulated with an oscillator. Also, we calculate the maximum dynamic evolution of the quantum states that changes the computation rate, and as an important achievement of this work, we show that for even-order perturbation, the rate of complexity increases, while for odd-order perturbation, the rate We will have a decreasing behavior. This method can be considered as a theoretical model for the upper limit of calculations.
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