Permanent Persistent Turing Machine: A new Model for Interactive Computation

Abstract

Since the computation of human life is in the progress rapidly and there is interaction in their computational process, we need to offer new concepts in computational theory, especially in the interactive computation to obviate these needs. In this paper, we introduce a new model for interactive computation. First, we briefly review interactive computation concept. Then, we provide and explain Persistent Turing Machine, as a model for interactive computation. There are some disadvantages in definitions of this model. For example, there is not functional property in the computational process of these models. As well as, the language which was accepted by this model, defined as a set of streams. Whereas, in other computational models, we use a set of strings, for indicating the language which was accepted by a model. As a result, we cannot compare the languages were accepted by these models, with the other models and their languages. Next, we propose Permanent Persistent Turing Machine (PPTM), as a model of interactive computation, so that, eliminate these disadvantages. After that, we define sets and relationships were accepted by the PPTMs and introduce their properties in details. Finally, we compare the computational power of this model with other classical models; and we prove that the computational power of the proposed model is more than Turing machine and it can compute some problems, which are not computed by Turing machine.

Keywords

• Interactive Computation,Permanent Persistent Turing Machine,Persistent Turing Machine,Permanent Recursive Languages,Permanent Recursive Enumerable Languages

References

1. [1] Goldin, Dina, Scott A. Smolka, and Peter Wegner, eds. Interactive computation: The new paradigm. Springer Science & Business Media, 2006.
2. [2] Goldin, Dina Q., Scott A. Smolka, Paul C. Attie, and Elaine L. Sonderegger. "Turing machines, transition systems, and interaction." Information and Computation 194, no. 2 (2004): 101-128.
3. [3] Wegner, Peter. "Interactive foundations of computing." Theoretical computer science 192, no. 2 (1998): 315-351.
4. [4] Syropoulos, Apostolos. Hypercomputation: computing beyond the Church-Turing barrier. Springer Science & Business Media, 2008.
5. [5] Goldin, Dina Q. "Persistent Turing machines as a model of interactive computation." In International Symposium on Foundations of Information and Knowledge Systems, pp. 116-135. Springer, Berlin, Heidelberg, 2000.
6. [6] Wegner, Peter. "Interactive foundations of computing." Theoretical computer science 192, no. 2 (1998): 315-351.
7. [7] Cooper, B. S. "Computability Theory. Chapman Hall/Crc Mathematics Series." (2003).
8. [8] Davis, Martin, Ron Sigal, and Elaine J. Weyuker. Computability, complexity, and languages: fundamentals of theoretical computer science. Newnes, 1994.

9. [9] Ord, Toby. "Hypercomputation: computing more than the Turing machine." arXiv preprint math/0209332 (2002).
10. [10] Copeland, B. Jack. "The church-turing thesis." Stanford encyclopedia of philosophy (2002).
11. [11] Kolan, Amy J. "Interactive Computation for Undergraduates: The Next Generation." Journal of Statistical Physics 167, no. 3-4 (2017): 997-1006.
12. [12] Kosub, Sven. Persistent computations. Inst. für Informatik, 1998.
13. [13] Luttik, Bas, and Fei Yang. "On the Executability of Interactive Computation." In Conference on Computability in Europe, pp. 312-322. Springer International Publishing, 2016.