Computer Language
Small universal Turing machines
Theoretical Computer Science - Special issue on universal machines and computations
Frontier between decidability and undecidability: a survey
Theoretical Computer Science - Special issue on universal machines and computations
Small Universal One-State Linear Operator Algorithm
MFCS '92 Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science
A Universal Turing Machine with 3 States and 9 Symbols
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
Small turing machines and generalized busy beaver competition
Theoretical Computer Science
Computation: finite and infinite machines
Computation: finite and infinite machines
The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions
On the time complexity of 2-tag systems and small universal Turing machines
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Study of limits of solvability in tag systems
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
Four small universal turing machines
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
Solvability of the Halting and Reachability Problem for Binary 2-tag Systems
Fundamenta Informaticae
Study of limits of solvability in tag systems
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
Solvability of the Halting and Reachability Problem for Binary 2-tag Systems
Fundamenta Informaticae
On the complex behavior of simple tag systems-An experimental approach
Theoretical Computer Science
Turing computability and membrane computing
CMC'12 Proceedings of the 13th international conference on Membrane Computing
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Tag systems were invented by Emil Leon Post and proven recursively unsolvable by Marvin Minsky. These production systems have proved to be 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 and the number of symbols @m. 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+1-problem to a surprisingly small tag system. It indicates that the present unsolvability line-defined in terms of @m and v-for tag systems might be significantly decreased.