This is a talk on minicomplexity, namely on the complexity of two-way finite automata. We start with a smooth introduction to its basic concepts, which also brings together several seemingly detached, old theorems. We then record recent advances, both in the theory itself and in its relation to Turing machine complexity. Finally, we illustrate a proof technique, which we call hardness propagation by certificates. The entire talk follows, extends, and advocates the Sakoda-Sipser framework.
KeywordsState Component Relational Match Relational Path Size Complexity Strong Conjecture
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