Alexander Okhotin

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This paper introduces a class of formal grammars made up by augmenting the formalism of context-free grammars with an explicit set-theoretic intersection operation. It is shown that conjunctive grammars can generate some important non-contextfree language constructs, including those not in the intersection closure of context-free languages, and that they(More)
It is proved that the set of scattered substrings of a language recognized by an n-state DFA requires a DFAwith at least 2 n 2−2 states (the known upper bound is 2), 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 complexity(More)
Nondeterministic finite automata (NFA) with at most one accepting computation on every input string are known as unambiguous finite automata (UFA). This paper considers UFAs over a one-letter alphabet, and determines the exact number of states in DFAs needed to represent unary languages recognized by n-state UFAs in terms of a new number-theoretic function(More)
Systems of equations of the form φj(X1, . . . ,Xn) = ψj(X1, . . . ,Xn) with 1 6 j 6 m are considered, in which the unknowns Xi are sets of natural numbers, while the expressions φj , ψj may contain singleton constants and the operations of union and pairwise addition S + T = {m + n | m ∈ S, n ∈ T}. It is shown that the family of sets representable by unique(More)