"[24D6D1C07644]" . . . "10.3233/FI-2011-540" . . . "Okhotin, Alexander" . "RIV/00216224:14310/11:00050220!RIV12-GA0-14310___" . "RIV/00216224:14310/11:00050220" . . "Kunc, Michal" . . . "The number of states in a two-way nondeterministic finite automaton (2NFA) needed to represent intersection of languages given by an m-state 2NFA and an n-state 2NFA is shown to be at least m + n and at most m + n + 1. For the union operation, the number of states is exactly m + n. The lower bound is established for languages over a one-letter alphabet. The key point of the argument is the following number-theoretic lemma: for all m,n >= 2 with m, n not equal to 6 (and with finitely many other exceptions), there exist partitions m = p1 +...+ pk and n = q1 +...+ ql, where all numbers p1,...,pk,q1,...,ql >= 2 are powers of pairwise distinct primes. For completeness, an analogous statement about partitions of any two numbers m,n not in {4,6} (with a few more exceptions) into sums of pairwise distinct primes is established as well." . "State complexity of union and intersection for two-way nondeterministic finite automata" . "Fundamenta Informaticae" . "232151" . "The number of states in a two-way nondeterministic finite automaton (2NFA) needed to represent intersection of languages given by an m-state 2NFA and an n-state 2NFA is shown to be at least m + n and at most m + n + 1. For the union operation, the number of states is exactly m + n. The lower bound is established for languages over a one-letter alphabet. The key point of the argument is the following number-theoretic lemma: for all m,n >= 2 with m, n not equal to 6 (and with finitely many other exceptions), there exist partitions m = p1 +...+ pk and n = q1 +...+ ql, where all numbers p1,...,pk,q1,...,ql >= 2 are powers of pairwise distinct primes. For completeness, an analogous statement about partitions of any two numbers m,n not in {4,6} (with a few more exceptions) into sums of pairwise distinct primes is established as well."@en . "1-4" . . . "0169-2968" . "1"^^ . "P(GA201/09/1313)" . . . "2"^^ . "NL - Nizozemsko" . . "State complexity of union and intersection for two-way nondeterministic finite automata" . . . . "110" . "finite automata; two-way automata; state complexity; partitions into sums of primes"@en . . "14310" . "000294764900018" . "9"^^ . "State complexity of union and intersection for two-way nondeterministic finite automata"@en . . "State complexity of union and intersection for two-way nondeterministic finite automata"@en .