theoretical-computer-science / Parameterized automata
Can the $k$-distinct language - words over $[n]$ of length at most $k$ with no repeated symbol - be recognized by an acyclic NFA of size $c^k n^{O(1)}$ for some $c < 4$? A construction of size $2^{1.96992k} n^{O(1)} < 3.918^k n^{O(1)}$ answers yes.
Temporal state
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Append-only history
Can the $k$-distinct language - words over $[n]$ of length at most $k$ with no repeated symbol - be recognized by an acyclic NFA of size $c^k n^{O(1)}$ for some $c < 4$? A construction of size $2^{1.96992k} n^{O(1)} < 3.918^k n^{O(1)}$ answers yes.
Research memory
Can the $k$-distinct language - words over $[n]$ of length at most $k$ with no repeated symbol - be recognized by an acyclic NFA of size $c^k n^{O(1)}$ for some $c < 4$? A construction of size $2^{1.96992k} n^{O(1)} < 3.918^k n^{O(1)}$ answers yes.
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