Finite state incompressible infinite sequences

Cristian S. Calude, Ludwig Staiger, Frank Stephan
2016 Information and Computation  
Motivation The incomputability of all descriptional complexities is an obstacle towards more "down-to-earth" applications of AIT (e.g. for practical compression). To avoid incomputability we can restrict the resources available to the universal Turing machine, or restrict the computational power of the machines used (e.g. use context-free grammars or straight-line programs) instead of Turing machines. Here we use the second approach with finite transducers instead of Turing machines. The lack
more » ... a universal finite transducer is not an obstacle. Finite State Incompressible Infinite Sequences 2 / 21 Motivation The incomputability of all descriptional complexities is an obstacle towards more "down-to-earth" applications of AIT (e.g. for practical compression). To avoid incomputability we can restrict the resources available to the universal Turing machine, or restrict the computational power of the machines used (e.g. use context-free grammars or straight-line programs) instead of Turing machines. Here we use the second approach with finite transducers instead of Turing machines. The lack of a universal finite transducer is not an obstacle. Finite State Incompressible Infinite Sequences 2 / 21 Motivation The incomputability of all descriptional complexities is an obstacle towards more "down-to-earth" applications of AIT (e.g. for practical compression). To avoid incomputability we can restrict the resources available to the universal Turing machine, or restrict the computational power of the machines used (e.g. use context-free grammars or straight-line programs) instead of Turing machines. Here we use the second approach with finite transducers instead of Turing machines. The lack of a universal finite transducer is not an obstacle. Finite State Incompressible Infinite Sequences 2 / 21 Motivation The incomputability of all descriptional complexities is an obstacle towards more "down-to-earth" applications of AIT (e.g. for practical compression). To avoid incomputability we can restrict the resources available to the universal Turing machine, or restrict the computational power of the machines used (e.g. use context-free grammars or straight-line programs) instead of Turing machines. Here we use the second approach with finite transducers instead of Turing machines.
doi:10.1016/j.ic.2015.11.003 fatcat:g3p6qls62nc6hl2mp4ahsntsuy