## Post’s system of tag – A simple discrete nonlinear system (1992)

Venue: | Center for Theoretical Physics, University of Twente, Enschede, The Netherlands |

Citations: | 1 - 1 self |

### BibTeX

@INPROCEEDINGS{Asveld92post’ssystem,

author = {Peter R. J. Asveld},

title = {Post’s system of tag – A simple discrete nonlinear system},

booktitle = {Center for Theoretical Physics, University of Twente, Enschede, The Netherlands},

year = {1992},

pages = {26--31}

}

### OpenURL

### Abstract

Abstract − We consider an instance T 0 of Post’s system of tag for which we show that it is nonlinear. Then we discuss some computer simulations and study the periodic behavior of T 0. 1.

### Citations

97 |
The 3x + 1 problem and its generalizations
- Lagarias
- 1985
(Show Context)
Citation Context .... � d i ⋅ 2 i In essence T 0 has the same structure as a younger but more famous simple nonlinear system, viz. The 3x + 1 problem. (Also: Ulam’s problem, Collatz’s problem, the Syracuse problem, etc. =-=[4]-=-): � v t / 2 if v t is even, � v t + 1 = � � 3 ⋅ v t + 1 if v t is odd. � The 3x + 1 conjecture. For each initial value v 0 (v 0∈IN) the ultimate behavior of v t is the 3-cycle . . . ⇒ 4 ⇒ 2 ⇒ 1 ⇒ 4 .... |

93 |
Recursive unsolvability of Post’s problem of “tag” and other topics in theory of Turing machines
- Minsky
- 1961
(Show Context)
Citation Context ...s from ω′ t; this yields ω t +1. Post’s systems of tag have been introduced in [7,8]; cf. [6] for an introduction. They are quite powerful, since they are able to simulate Turing-machine computations =-=[5]-=- and thus to perform every effective computation. However, in this note we restrict our attention to a single simple instance T 0 of such a system (§2). In §3 we show that this instance is nonlinear. ... |

82 |
Formal Reduction of the General Combinatorial Decision Problem
- Post
(Show Context)
Citation Context ...ring P (σ) to the right end of ω t. We denote the string obtained in this fashion by ω′ t. � We delete the first d symbols from ω′ t; this yields ω t +1. Post’s systems of tag have been introduced in =-=[7,8]-=-; cf. [6] for an introduction. They are quite powerful, since they are able to simulate Turing-machine computations [5] and thus to perform every effective computation. However, in this note we restri... |

34 |
Absolutely Unsolvable Problems and Relatively Undecidable Propositions - Account of an Anticipation
- Post
- 1965
(Show Context)
Citation Context ...ring P (σ) to the right end of ω t. We denote the string obtained in this fashion by ω′ t. � We delete the first d symbols from ω′ t; this yields ω t +1. Post’s systems of tag have been introduced in =-=[7,8]-=-; cf. [6] for an introduction. They are quite powerful, since they are able to simulate Turing-machine computations [5] and thus to perform every effective computation. However, in this note we restri... |

4 |
Periodicity of Post’s normal process of tag
- Watanabe
- 1963
(Show Context)
Citation Context ...k, ω0 explodes: � ωt � → ∞ as t → ∞. � Of the simple instances of Post’s system of tag the following one — already studied by Post in 1921-1922; cf. [8] — is one of the simplest nontrivial cases; cf. =-=[1,2,3,6,7,8,9,10]-=-. The remaining part of this note is devoted to this instance. Example 2.2. Consider T 0 = (Σ,d,P, ω0) with Σ = {0,1}, d = 3, P (0) = 00 and P (1) = 1101. Examples of its behavior are in Figure 1 for ... |

3 |
Tag systems and lag systems
- Wang
- 1963
(Show Context)
Citation Context ...k, ω0 explodes: � ωt � → ∞ as t → ∞. � Of the simple instances of Post’s system of tag the following one — already studied by Post in 1921-1922; cf. [8] — is one of the simplest nontrivial cases; cf. =-=[1,2,3,6,7,8,9,10]-=-. The remaining part of this note is devoted to this instance. Example 2.2. Consider T 0 = (Σ,d,P, ω0) with Σ = {0,1}, d = 3, P (0) = 00 and P (1) = 1101. Examples of its behavior are in Figure 1 for ... |

2 | On a Post’s system of tag
- Asveld
- 1988
(Show Context)
Citation Context ...k, ω0 explodes: � ωt � → ∞ as t → ∞. � Of the simple instances of Post’s system of tag the following one — already studied by Post in 1921-1922; cf. [8] — is one of the simplest nontrivial cases; cf. =-=[1,2,3,6,7,8,9,10]-=-. The remaining part of this note is devoted to this instance. Example 2.2. Consider T 0 = (Σ,d,P, ω0) with Σ = {0,1}, d = 3, P (0) = 00 and P (1) = 1101. Examples of its behavior are in Figure 1 for ... |

2 |
On Post’s system of tag with 0 → 00 and 1 → 1101 as productions, Memoranda Informatica (in preparation
- Asveld
(Show Context)
Citation Context |

1 |
A simple system with chaotic behavior, Memoranda Informatica 88-51 (Dept. of Comp. Sci., Twente University of Technology). Also in: D. Kleima et al (Eds.): Liber Amicorum for E.W. Gröneveld
- Asveld
- 1988
(Show Context)
Citation Context |