TY  - EJOU
AU  - Cha, Reeseo 
AU  - Nam, Wonhong 
AU  - Choi, Jin-Young 

TI  - Reliable Approximated Number System with Exact Bounds and Three-Valued Logic
T2  - Computer Systems Science and Engineering

PY  - 2018
VL  - 33
IS  - 6
SN  - 

AB  - Many programming languages provides mechanism to guarantee the error ranges of exact numbers and intervals. However, when they are integrated with
unreliable approximated numbers, we cannot rely on the error-ranges anymore. Such unreliable error-ranges may cause serious errors in programs, and
especially in safety critical systems they cost us huge amount of money and/or threaten human’s life. Hence, in this paper, we propose a novel number system
to safely perform arithmetic operations with guaranteed error ranges. In the number system, exact numbers are separated from approximated numbers, and
approximated numbers with strictly guaranteed error-ranges are again separated from unwarranted numbers such as floating-point numbers. A three-valued
logic is also shipped with our number system to appropriately deal with uncertainties due to approximations. A prototype implementation of our number
system in Python is demonstrated. With this module, we can more reliably execute operations on numbers and make judgments on the conditions involving
numbers.
KW  - Formal Methods
KW  -  Approximated Number System
KW  -  Exact Bounds
KW  -  Three-valued Logic

DO  - 10.32604/csse.2018.33.447