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A new generalization of context-free grammars is introduced: Boolean grammars allow the use of all set-theoretic operations as an integral part of the formalism of rules. Rigorous semantics for these grammars is defined by language equations in a way that allows to generalize some techniques from the theory of context-free grammars, including Chomsky normal(More)
It is proved that the set of scattered substrings of a language recognized by an n-state DFA requires a DFA with at least 2 n 2 −2 states (the known upper bound is 2 n), with witness languages given over an exponentially growing alphabet. For a 3-letter alphabet, scattered substrings are shown to require at least 2 √ 2n+30−6 states. A similar state(More)
It has recently been proved (Je˙ z, DLT 2007) that conjunctive grammars (that is, context-free grammars augmented by conjunction) generate some non-regular languages over a one-letter alphabet. The present paper improves this result by constructing conjunctive grammars for a larger class of unary languages. The results imply undecidability of a number of(More)