We develop a new algebraic technique that gives a simple randomized algorithm for the simple $k$-path problem with the same complexity $O^*(1.657^k)$ as in [A. Bj\"orklund. Determinant Sums for Undirected Hamiltonicity. FOCS 2010, pp. 173--182, (2010). A. Bj\"orklund, T. Husfeldt, P. Kaski, M. Koivisto. Narrow sieves for parameterized paths and ... more >>>

In this paper we first show that Tester for an $F$-algebra $A$
and multilinear forms (see Testers and their Applications ECCC 2012) is equivalent to multilinear
algorithm for the product of elements in $A$
(see Algebraic
complexity theory. vol. 315, Springer-Verlag). Our
result is constructive in deterministic polynomial time. ... more >>>

Communication complexity of XOR functions $f (x \oplus y)$ has attracted increasing attention in recent years, because of its connections to Fourier analysis, and its exhibition of exponential separations between classical and quantum communication complexities of total functions.However, the complexity of certain basic functions still seems elusive especially in the ... more >>>