Interval-valued computation is a special kind of theoretical models for computation. It is capable of working on “interval-valued bytes”: special subsets of the unit interval. Thus, this model can be regarded as kind of ideal analog computer. If such computers were realized, their computation power would be much greater than that of functioning, "implementable" computers. As such, there are no architectures for their physical implementations. Only special subsets of the unit interval are concerned, the restrictios are of finite nature, thusthe paradigm fits into the framework of Church-Turing thesis,[1] unlike real computation
Such a model of computation is capable of solving NP-complete problems like tripartite matching.[2] “The validity problem of quantified propositional formulae is decidable by a linear interval-valued computation. As a consequence, all polynomial space problems are decidable by a polynomial interval-valued computation. Furthermore, it is proven that PSPACE coincides with the class of languages which are decidable by a restricted polynomial interval-valued computation” (links added).[3]
See also
Notes
References
- Nagy, Benedek (23 September 2007). "Visual reasoning by generalized interval-values and interval temporal logic" (PDF). In Philip T. Cox & Andrew Fish & John Howse (ed.). VLL. Proceedings of the VLL 2007 workshop on Visual Languages and Logic. Coeur d'Aléne, Idaho, USA: CEUR Workshop Proceedings. pp. 13–26.
{{cite conference}}: Unknown parameter|booktitle=ignored (|book-title=suggested) (help); Unknown parameter|coauthors=ignored (|author=suggested) (help) - Nagy, Benedek (April 8, 2008). "Interval-valued computations and their connection with PSPACE". Theoretical Computer Science (Preface: From Gödel to Einstein: Computability between Logic and Physics). 394 (3): 208–222.
{{cite journal}}: Unknown parameter|coauthors=ignored (|author=suggested) (help) - Tajti, Ákos (June 20, 2008). Solving Tripartite Matching by Interval-valued Computation in Polynomial Time. Computability in Europe 2008. Logic and Theory of Algorithms. pp. 208–222.
{{cite conference}}: External link in|conferenceurl=|coauthors=ignored (|author=suggested) (help); Unknown parameter|conferenceurl=ignored (|conference-url=suggested) (help) See short abstract.
External links
- Nagy, Benedek (23 September 2007). "Visual reasoning by generalized interval-values and interval temporal logic" (PDF). In Philip T. Cox & Andrew Fish & John Howse (ed.). VLL. Proceedings of the VLL 2007 workshop on Visual Languages and Logic. Coeur d'Aléne, Idaho, USA: CEUR Workshop Proceedings. pp. 13–26.
{{cite conference}}: Unknown parameter|booktitle=ignored (|book-title=suggested) (help); Unknown parameter|coauthors=ignored (|author=suggested) (help)
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