Abstract
The algebraic theory of finite automata has developed into a well-structured field, with the notion of variety serving as the unifying concept. Of course, the class of regular languages is very restricted and, for that reason, has not so far played any significant role in computational complexity. The connections between automata and complexity that have been presented in this paper give evidence that some ideas and results from the restricted theory can fruitfully be adapted to investiate more general questions. It is our belief that these connections are not mere coincidences and that the systematic classification available for finite automata and regular languages can be helpful in organizing our knowledge about computations and in suggesting new directions for further research.
Research supported by National Science Foundation Grant CCR-8700700
Research supported by grants from NSERC and FCAR
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Straubing, H., Thérien, D. (1989). Finite automata and computational complexity. In: Pin, J.E. (eds) Formal Properties of Finite Automata and Applications. LITP 1988. Lecture Notes in Computer Science, vol 386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013122
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DOI: https://doi.org/10.1007/BFb0013122
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