Reliable Approximated Number System with Exact Bounds and Three-valued Logic
- Authors
- Cha, Reeseo; Nam, Wonhong; Choi, Jin-Young
- Issue Date
- 11월-2018
- Publisher
- C R L PUBLISHING LTD
- Keywords
- Formal Methods; Approximated Number System; Exact Bounds; Three-valued Logic
- Citation
- COMPUTER SYSTEMS SCIENCE AND ENGINEERING, v.33, no.6, pp.447 - 455
- Indexed
- SCIE
SCOPUS
- Journal Title
- COMPUTER SYSTEMS SCIENCE AND ENGINEERING
- Volume
- 33
- Number
- 6
- Start Page
- 447
- End Page
- 455
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/72044
- ISSN
- 0267-6192
- Abstract
- 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
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