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Circuit Complexity of Regular Languages

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We survey the current state of knowledge on the circuit complexity of regular languages and we prove that regular languages that are in AC0 and ACC0 are all computable by almost linear size circuits, extending the result of Chandra et al. (J. Comput. Syst. Sci. 30:222–234, 1985). As a consequence we obtain that in order to separate ACC0 from NC1 it suffices to prove for some ε>0 an Ω(n 1+ε) lower bound on the size of ACC0 circuits computing certain NC1-complete functions.

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  1. Institute of Mathematics, Academy of Sciences of Czech Republic, Žitná 25, 115 67, Praha 1, Czech Republic

    Michal Koucký

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  1. Michal Koucký
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Correspondence to Michal Koucký.

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Partially supported by grant GA ČR 201/07/P276, project No. 1M0021620808 of MŠMT ČR and Institutional Research Plan No. AV0Z10190503.

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Koucký, M. Circuit Complexity of Regular Languages. Theory Comput Syst 45, 865–879 (2009). https://doi.org/10.1007/s00224-009-9180-z

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