The logic blocks of most modern FPGAs contain clusters of look-up tables and flip flops, yet little is known about good choices for several key architectural parameters related to these clusters. There are three basic questions: how many look-up tables should a cluster contain, how should the flexibility of FPGA routing change as the cluster size changes, and how many inputs should the programm...

The associativity problem for the class of finite multiplication tables is known to be undecidable, even for quite narrow infinite subclasses of tables. We present criteria which can be used to decide associativity in many cases, although any effective method based on such criteria must eventually fail on a table of some size (as otherwise decidability for the general class would follow). By me...