# Operations on Self-Verifying Finite Automata

## Abstract

We investigate the complexity of regular operations on languages represented by self-verifying automata. We get the tight bounds for complement, intersection, union, difference, symmetric difference, reversal, star, left and right quotients, and asymptotically tight bound for concatenation. To prove tightness, we use a binary alphabet in the case of boolean operations and reversal, and an alphabet that grows exponentially for the remaining operations. However, we also provide exponential lower bounds for these operations using a fixed alphabet.

## Notes

### Acknowledgments

We would like to thank Peter Eliáš for his help with the reversal operation. We are also very grateful to an anonymous referee of CSR for careful reading of the paper and for pointing out an error in a previous draft of Fig. 1.

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