2014/03/16 by Vojtěch Vorel, Vorel, Vojtěch
Biochemistry, Genetics and Molecular Biology · Computer Science · #DNA and Biological Computing #Formal Methods in Verification #cs.FL #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1403.3972
An extended version of the paper "Subset Synchronization of Transitive Automata" presented at AFL 2014
arxiv created 2016/02/15 · arxiv updated 2016/02/16
We present a strongly exponential lower bound that applies both to the subset synchronization threshold for binary deterministic automata and to the careful synchronization threshold for binary partial automata. In the later form, the result finishes the research initiated by Martyugin (2013). Moreover, we show that both the thresholds remain strongly exponential even if restricted to strongly connected binary automata. In addition, we apply our methods to computational complexity. Existence of a subset reset word is known to be PSPACE-complete; we show that this holds even under the restriction to strongly connected binary automata. The results apply also to the corresponding thresholds in two more general settings: D1- and D3-directable nondeterministic automata and composition sequences over finite domains.