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. 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 considered, the restrictions are of finite nature, causing that the computation power of this paradigm fits into the framework of Church-Turing thesis: unlike real computation, interval-valued computation is not capable of hypercomputation, is not corresponding to an unrestricted ideal analog computer.

Such a model of computation is capable of solving NP-complete problems like tripartite matching. “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).

Notes

References

• Nagy, Benedek; Vályi, Sándor "Visual reasoning by generalized interval-values and interval temporal logic". VLL, 13–26. .
• Nagy, Benedek; Vályi, Sándor "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.
• Tajti, Ákos; Nagy, Benedek "Solving Tripartite Matching by Interval-valued Computation in Polynomial Time". , 208–222. . See short abstract

External links

• Nagy, Benedek; Vályi, Sándor "Visual reasoning by generalized interval-values and interval temporal logic". VLL, 13–26. .