Independence results in computer science?

Joseph, Deborah; Young, Paul R.

doi:10.1016/0022-0000(81)90013-1

Cited by 14 publications

(4 citation statements)

References 22 publications

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“…Notice that we recently discovered that in older papers it had been noted that undecidability and incompleteness in automata theory were intimately related and that one could for instance obtain some results about automata which are true but unprovable in some recursive theory extending Peano Arithmetic like ZFC, [Har85,JY81]. However the results presented here, although they are not very difficult to prove, exhibit in our opinion the following novelties:…”

Section: Introductionmentioning

confidence: 56%

Incompleteness Theorems, Large Cardinals, and Automata Over Finite Words

Finkel

2019

Int. J. Found. Comput. Sci.

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We prove that one can construct various kinds of automata over finite words for which some elementary properties are actually independent from strong set theories like [Formula: see text] [Formula: see text] “There exist (at least) [Formula: see text] inaccessible cardinals”, for integers [Formula: see text]. In particular, we prove independence results for languages of finite words generated by context-free grammars, or accepted by 2-tape or 1-counter automata. Moreover we get some independence results for weighted automata and for some related finitely generated subsemigroups of the set [Formula: see text] of 3-3 matrices with integer entries. Some of these latter results are independence results from the Peano axiomatic system PA.

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Section: Introductionmentioning

confidence: 56%

Incompleteness Theorems, Large Cardinals, and Automata Over Finite Words

Finkel

2019

Int. J. Found. Comput. Sci.

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“…However, at the beginning of the growth of computer science, it still faced obstacles in teaching to operate computers even though various languages adapted to the environment [52]. The deficiency triggered by the axiomatic basis of computer science based on arithmetic theory is weak [53]. One of the approaches offered is to choose a teaching module that suits the learner's interests and background [54].…”

Section: A Material: From Concept To Science or Technologymentioning

confidence: 99%

Computer Science

Nasution¹,

Hidayat²,

Syah³

2022

International Journal on Advanced Science, Engineering and Information Technology

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Possible for science itself, conceptually, to have and will understand differently, let alone science also seen as technology, such as computer science. After all, science and technology are viewpoints diverse by either individual, community, or social. Generally, it depends on socioeconomic capabilities. So it is with computer science has become a phenomenon and fashionable, where based on the stream of documents, various issues arise in either its theory or implementation, adapting different communities, or designing curriculum holds in the education system. Generally, there are gaps between rich and poor, masculine and feminine, and basic sciences, engineering, and social sciences in accessing and using computer science. In particular, there have been various developments in hardware, software, and brain-ware from computer science in the application. There are recurring problems shortly, in the same or different places, both in developed and technologically lagging countries. Although computer science is still new, it has provided various innovations through research, which is proven by many documents. Therefore, following the growth of computer science -documents in the reputable indexed database, Scopus -there are clues for showing the trends. That is, dividing documents into three-time sessions: sloping, increasing and decreasing. That is by using a growth graphic. Then equip it with some parameters: topics and the weights from hit counts of databases. It gives the meaning as an interpretation to support the reviews. Therefore, this paper will provide a commentary related to that growth. It is for showing that despite the spread of studies, at the last time-session, the issues were always present simultaneously at the same time in accumulation. That is for describing a study title of computer science about what the world already has, going, and will understand about computer science. It is a view regarding its philosophy, basic science, applications, and technology as concepts and solutions that make computer science the primary foundation for skills and professions in the 21 st century through the education system. Therefore, other scientific fields such as informatics, computer engineering, information science, information technology, and data science, which are at the crossroads of computer science, are also scientific fields that raise different issues.

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“…Hypersimple sets are crucial in a surprising characterization of recursively axiomatizable theories that have no independent recursive axiomatization [Kre57,PE68]. Furthermore, hypersimple sets have played a role in independence results for both complexity theory [JY81] and control structures [Roy87]. We expect that an important understanding of the role of hypersimple sets in separation and independence in general can be obtained by a careful comparative study of the examples referenced in this paragraph.…”

Section: Introductionmentioning

confidence: 97%