منابع مشابه
Nonstandard arithmetic and recursive comprehension
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...
متن کاملArithmetic Algorithms for Ternary Number System
The use of multi-valued logic in VLSI circuits can reduce the chip area significantly. Moreover, there are several additional advantages of using multi-valued logic in VLSI over the conventional Binary logic, such as energy efficiency, cost-effectiveness and so on. It has been shown that Base-3 number system is nearly optimal for computation. This paper is composed of two parts. In the first pa...
متن کاملArithmetic Ternary Decision Diagrams Applications and Complexity
In a binary decision diagram (BDD), a non-terminal node representing a function f = xf0_xf1 has two edges for f0 and f1. In the arithmetic ternary decision diagram (Arith TDD), each non-terminal node has three edges, where the third edge denotes f2 = f0 + f1, and + is an integer addition. The Arith TDD represents the extended weight function, an integer function showing the numbers of true mint...
متن کاملRecursive Double-Size Fixed Precision Arithmetic
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...
متن کاملFormalized Interpretability in Primitive Recursive Arithmetic
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1962
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-10528