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Tag systems and Collatzlike functions
"... Tag systems were invented by Emil Leon Post and proven recursively unsolvable by Marvin Minsky. These production systems have shown very useful in constructing small universal (Turing complete) systems for several different classes of computational systems, including Turing machines, and are thus im ..."
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Tag systems were invented by Emil Leon Post and proven recursively unsolvable by Marvin Minsky. These production systems have shown very useful in constructing small universal (Turing complete) systems for several different classes of computational systems, including Turing machines, and are thus important instruments for studying limits or boundaries of solvability and unsolvability. Although there are some results on tag systems and their limits of solvability and unsolvability, there are hardly any that consider both the shift number v, as well as the number of symbols µ. This paper aims to contribute to research on limits of solvability and unsolvability for tag systems, taking into account these two parameters. The main result is the reduction of the 3n + 1problem to a surprisingly small tag system. It indicates that the present unsolvability line – defined in terms of µ and v – for tag systems might be significantly decreased. Key words: Tag Systems, limits of solvability and unsolvability, universality,
Post’s system of tag – A simple discrete nonlinear system
 Center for Theoretical Physics, University of Twente, Enschede, The Netherlands
, 1992
"... 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. ..."
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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.
Solvability of the Halting and Reachability Problem for Tag systems with µ = v = 2
"... In this report we will provide a detailed proof of the solvability of the halting and reachability problem for 2symbolic tag systems with a shiftnumber v = 2. 1 ..."
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In this report we will provide a detailed proof of the solvability of the halting and reachability problem for 2symbolic tag systems with a shiftnumber v = 2. 1
A Simple Discrete System with Chaotic Behavior*
"... Abstract — We discuss the behavior of a particular discrete system, viz. Post’s system of tag with alphabet {0,1}, deletion number d = 3, and rules: 0 → 00, 1 → 1101. As initial string we consider all strings of length less than or equal to 15 as well as all ‘‘worst case’ ’ inputs of the form (100) ..."
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Abstract — We discuss the behavior of a particular discrete system, viz. Post’s system of tag with alphabet {0,1}, deletion number d = 3, and rules: 0 → 00, 1 → 1101. As initial string we consider all strings of length less than or equal to 15 as well as all ‘‘worst case’ ’ inputs of the form (100) m with 1 ≤ m ≤ 128. 1.