We describe a RAM algorithm computing all runs (=maximal repetitions) of a given string of length n over a general ordered alphabet in O(n log 2 3 n) time and linear space. Our algorithm outperforms all known solutions working in Θ(n log σ) time provided σ = n, where σ is the number of distinct letters in the input string. We conjecture that there exists a linear time RAM algorithm finding all ...

Let S be a planar n-point set. Classically, one can find the Voronoi diagram VD(S) for S in O(n log n) time and O(n) space. We study the situation when the available workspace is limited: for s ∈ {1, . . . , n}, an s-workspace algorithm has read-only access to an input array with the points from S in arbitrary order, and it may use only O(s) additional words of Θ(log n) bits for reading and wri...

We consider conversions of regular expressions into k-realtime finite state automata, i.e., automata in which the number of consecutive uses of ε-transitions, along any computation path, is bounded by a fixed constant k. For 2-realtime automata, i.e., for automata that cannot change the state, without reading an input symbol, more than two times in a row, we show that the conversion of a regula...

We give a new upper bound for the Group and Quasigroup Isomorphism problems when the input structures are given explicitly by multiplication tables. We show that these problems can be computed by polynomial size nondeterministic circuits of unbounded fan-in with O(log log n) depth and O(log n) nondeterministic bits, where n is the number of group elements. This improves the existing upper bound...

The running time is O(r log n). It can be shown by elementary means that the required r exists in O(log n). So the running time is O(log n). Moreover, by Fouvry’s Theorem [8], such r exists in O(log n), so the running time becomes O(log n). In [10], Lenstra and Pomerance showed that the AKS primality test can be improved by replacing the polynomial x − 1 in equation (1.1) with a specially const...

We investigate the computational complexity of languages which have interactive proof systems of bounded message complexity. In particular, denoting the length of the input by n, we show that If L has an interactive proof in which the total communication is bounded by c(n) bits then L can be recognized by a probabilistic machine in time exponential in O(c(n) + log(n)). If L has a public-coin in...