RANK LOGIC IS DEAD, LONG LIVE RANK LOGIC!

Rank Logic is Dead, Long Live Rank Logic!

Motivated by the search for a logic for polynomial time, we study rank logic (FPR) which extends fixed-point logic with counting (FPC) by operators that determine the rank of matrices over finite fields. While FPR can express most of the known queries that separate FPC from Ptime, nearly nothing was known about the limitations of its expressive power. In our first main result we show that the e...

Symmetric Circuits for Rank Logic

Fixed-point logic with rank (FPR) is an extension of fixed-point logic with counting (FPC) with operators for computing the rank of a matrix over a finite field. The expressive power of FPR properly extends that of FPC and is contained in PTime, but not known to be properly contained. We give a circuit characterization for FPR in terms of families of symmetric circuits with rank gates, along th...

Coalgebraic modal logic of finite rank

The TPP Is Dead, Long Live the TPP? A Response to Recent Commentaries

Distance Is Dead , Long Live Distance

For many educators, the phrase ‘from distance education to e-learning’ conjures up the view of an ‘evolutionary’ progression beginning with correspondence study and developed through more sophisticated technologies to its current identification with computers, the Internet, and the World Wide Web. For others, particularly those with little knowledge or experience of (and often equally little in...