Boolean function

Abstract: Boolean functions that satisfy higher order propagation criteria are studied. A complete characterization is given of the autocorrelation function and Walsh spectrum of second order functions. The number of second order functions satisfying PC(k) is related to a problem in coding theory and can be computed explicitly for k = 1, n - 1 and n. A new interpretation of the number of balanced second order functions is given and a class of functions showing interesting properties is discussed.

Abstract: A method is presented for determining whether a Boolean function possesses any group invariance; that is, whether there are any permutations or primings of the independent variables which leave the function unchanged This method is then extended to the detection of functions which are totally symmetric

Abstract: The issues of software compute time and complexity are very important in current computer-aided design (CAD) tools. As field-programmable gate array (FPGA) speeds and densities increase, the opportunity for effective hardware accelerators built from FPGA technology has opened up. This paper describes and evaluates a formula-specific method for implementing Boolean satisfiability solver circuits in configurable hardware. That is, using a template generator, we create circuits specific to the problem instance to be solved. This approach yields impressive runtime speedups of up to several hundred times compared to the software approaches. The high performance comes from realizing fine-grained parallelism inherent in the clause evaluation and implication and from direct mapping of Boolean relations into logic gates. Our implementation uses a commercially available hardware system for proof of concept. This system yields more than 100 times run-time speedup on many problems, even though the clock rate of the hardware is 100 times slower than that of the workstation running the software solver. While the time to compile the solver circuit to configurable hardware can he quite long on current platforms (20-40 min per chip), this paper discusses new approaches to overcome this compilation overhead. More broadly, we view this work as a case study in the burgeoning domain of high performance configurable computing. Our approach realizes large amount of fine-grained parallelism, and has broad applications in the very large scale integration CAD area.