Abstract
The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of regular languages is the maximal syntactic complexity of languages in that subclass, taken as a function of the state complexity n of these languages. We study the syntactic complexity of three subclasses of star-free languages. We find tight upper bounds for languages accepted by monotonic, partially monotonic and “nearly monotonic” automata; all three of these classes are star-free. We conjecture that the bound for nearly monotonic languages is also a tight upper bound for star-free languages.
This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant No. OGP0000871.
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Brzozowski, J., Li, B. (2012). Syntactic Complexities of Some Classes of Star-Free Languages. In: Kutrib, M., Moreira, N., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2012. Lecture Notes in Computer Science, vol 7386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31623-4_9
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DOI: https://doi.org/10.1007/978-3-642-31623-4_9
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