Abstract
We consider the power of nondeterministic finite automata with generalized acceptance criteria and the corresponding logics. In particular, we examine the expressive power of monadic second-order logic enriched with monadic second-order generalized quantifiers for algebraic word-problems. Extending a well-known result by Büchi, Elgot, and Trakhtenbrot, we show that considering monoidal quantifiers, the obtained logic captures the class of regular languages. We also consider monadic second-order groupoidal quantifiers and show that these are powerful enough to define every language in LOGCFL.
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Galota, M., Vollmer, H. (2001). A Generalization of the Büchi-Elgot-Trakhtenbrot Theorem. In: Fribourg, L. (eds) Computer Science Logic. CSL 2001. Lecture Notes in Computer Science, vol 2142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44802-0_25
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DOI: https://doi.org/10.1007/3-540-44802-0_25
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