A Multivariate Analysis of Some DFA Problems
- Cite this paper as:
- Fernau H., Heggernes P., Villanger Y. (2013) A Multivariate Analysis of Some DFA Problems. In: Dediu AH., Martín-Vide C., Truthe B. (eds) Language and Automata Theory and Applications. LATA 2013. Lecture Notes in Computer Science, vol 7810. Springer, Berlin, Heidelberg
We initiate a multivariate analysis of two well-known NPhard decision problems on DFAs: the problem of finding a short synchronizing word and that of finding a DFA on few states consistent with a given sample of the intended language and its complement. For both problems, we study natural parameterizations and classify them with the tools provided by Parameterized Complexity. Somewhat surprisingly, in both cases, rather simple FPT algorithms can be shown to be optimal, mostly assuming the (Strong) Exponential Time Hypothesis.
KeywordsDeterministic finite automata NP-hard decision problems synchronizing word consistency problem
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