Real-Time Simulation of Multihead Tape Units
Journal of the ACM (JACM)
Pattern matching in pseudo real-time
Journal of Discrete Algorithms
A black box for online approximate pattern matching
Information and Computation
Lower bounds for online integer multiplication and convolution in the cell-probe model
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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A Turing machine multiplies on-line if it receives its inputs low order digits first and it produces the k-th output digit before reading in the (k+1)-st inputs. We present a general method for converting any off-line multiplication algorithm which forms the product of two n-bit binary numbers in time F(n) into an on-line method, and the new algorithm requires time only 0(F(n) log n). Applying this technique to the fast multiplication algorithm of Schönhage and Strassen gives an upper bound of 0(n (log n)2 log log n) for on-line multiplication of integers. Other applications are to the on-line problems of products of polynomials over a finite ring, recognition of palindromes, and multiplication by a constant.