GF(2)-grammars, recently introduced by Bakinova et al. (“ Formal languages over GF(2) ”, LATA 2018), are a variant of ordinary context-free grammars, in which the disjunction is replaced by exclusive OR, whereas the classical concatenation is replaced by a new operation called GF(2)-concatenation: KʘL is the set of all strings with an odd number of partitions into a concatenation of a string in K and a string in L. This paper establishes several results on the family of languages defined by these grammars. Over the unary alphabet, GF(2)-grammars define exactly the 2-automatic sets. No language of the form (formula Presented), with uniformly superlinear f, can be described by any GF(2)-grammar. The family is not closed under union, intersection, classical concatenation and Kleene star, non-erasing homomorphisms. On the other hand, this family is closed under injective nondeterministic finite transductions, and contains a hardest language under reductions by homomorphisms.
CITATION STYLE
Makarov, V., & Okhotin, A. (2019). On the expressive power of GF(2)-grammars. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11376 LNCS, pp. 310–323). Springer Verlag. https://doi.org/10.1007/978-3-030-10801-4_25
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